Optimization Books

Book SynopsisNew edition of a graduate-level textbook on that focuses on online convex optimization, a machine learning framework that views optimization as a process.In many practical applications, the environment is so complex that it is not feasible to lay out a comprehensive theoretical model and use classical algorithmic theory and/or mathematical optimization. Introduction to Online Convex Optimization presents a robust machine learning approach that contains elements of mathematical optimization, game theory, and learning theory: an optimization method that learns from experience as more aspects of the problem are observed. This view of optimization as a process has led to some spectacular successes in modeling and systems that have become part of our daily lives. Based on the “Theoretical Machine Learning” course taught by the author at Princeton University, the second edition of this widely used graduate level text features:Thoroughly updat

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Book SynopsisThis is an engaging and informative book on the modern practice of experimental design. The authors'' writing style is entertaining, the consulting dialogs are extremely enjoyable, and the technical material is presented brilliantly but not overwhelmingly. The book is a joy to read. Everyone who practices or teaches DOE should read this book. - Douglas C. Montgomery, Regents Professor, Department of Industrial Engineering, Arizona State University It''s been said: ''Design for the experiment, don''t experiment for the design.'' This book ably demonstrates this notion by showing how tailor-made, optimal designs can be effectively employed to meet a client''s actual needs. It should be required reading for anyone interested in using the design of experiments in industrial settings. Christopher J. Nachtsheim, Frank A Donaldson Chair in Operations Management, Carlson School of Management, University of Minnesota This book demonstraTable of ContentsPreface. Acknowledgments. 1 A simple comparative experiment. 1.1 Key concepts. 1.2 The setup of a comparative experiment. 1.3 Summary. 2 An optimal screening experiment. 2.1 Key concepts. 2.2 Case: an extraction experiment. 2.2.1 Problem and design. 2.2.2 Data analysis. 2.3 Peek into the black box. 2.3.1 Main-effects models. 2.3.2 Models with two-factor interaction effects. 2.3.3 Factor scaling. 2.3.4 Ordinary least squares estimation. 2.3.5 Significance tests and statistical power calculations. 2.3.6 Variance inflation. 2.3.7 Aliasing. 2.3.8 Optimal design. 2.3.9 Generating optimal experimental designs. 2.3.10 The extraction experiment revisited. 2.3.11 Principles of successful screening: sparsity, hierarchy, and heredity. 2.4 Background reading. 2.4.1 Screening. 2.4.2 Algorithms for finding optimal designs. 2.5 Summary. 3 Adding runs to a screening experiment. 3.1 Key concepts. 3.2 Case: an augmented extraction experiment. 3.2.1 Problem and design. 3.2.2 Data analysis. 3.3 Peek into the black box. 3.3.1 Optimal selection of a follow-up design. 3.3.2 Design construction algorithm. 3.3.3 Foldover designs. 3.4 Background reading. 3.5 Summary. 4 A response surface design with a categorical factor. 4.1 Key concepts. 4.2 Case: a robust and optimal process experiment. 4.2.1 Problem and design. 4.2.2 Data analysis. 4.3 Peek into the black box. 4.3.1 Quadratic effects. 4.3.2 Dummy variables for multilevel categorical factors. 4.3.3 Computing D-efficiencies. 4.3.4 Constructing Fraction of Design Space plots. 4.3.5 Calculating the average relative variance of prediction. 4.3.6 Computing I-efficiencies. 4.3.7 Ensuring the validity of inference based on ordinary least squares. 4.3.8 Design regions. 4.4 Background reading. 4.5 Summary. 5 A response surface design in an irregularly shaped design region. 5.1 Key concepts. 5.2 Case: the yield maximization experiment. 5.2.1 Problem and design. 5.2.2 Data analysis. 5.3 Peek into the black box. 5.3.1 Cubic factor effects. 5.3.2 Lack-of-fit test. 5.3.3 Incorporating factor constraints in the design construction algorithm. 5.4 Background reading. 5.5 Summary. 6 A "mixture" experiment with process variables. 6.1 Key concepts. 6.2 Case: the rolling mill experiment. 6.2.1 Problem and design. 6.2.2 Data analysis. 6.3 Peek into the black box. 6.3.1 The mixture constraint. 6.3.2 The effect of the mixture constraint on the model. 6.3.3 Commonly used models for data from mixture experiments. 6.3.4 Optimal designs for mixture experiments. 6.3.5 Design construction algorithms for mixture experiments. 6.4 Background reading. 6.5 Summary. 7 A response surface design in blocks. 7.1 Key concepts. 7.2 Case: the pastry dough experiment. 7.2.1 Problem and design. 7.2.2 Data analysis. 7.3 Peek into the black box. 7.3.1 Model. 7.3.2 Generalized least squares estimation. 7.3.3 Estimation of variance components. 7.3.4 Significance tests. 7.3.5 Optimal design of blocked experiments. 7.3.6 Orthogonal blocking. 7.3.7 Optimal versus orthogonal blocking. 7.4 Background reading. 7.5 Summary. 8 A screening experiment in blocks. 8.1 Key concepts. 8.2 Case: the stability improvement experiment. 8.2.1 Problem and design. 8.2.2 Afterthoughts about the design problem. 8.2.3 Data analysis. 8.3 Peek into the black box. 8.3.1 Models involving block effects. 8.3.2 Fixed block effects. 8.4 Background reading. 8.5 Summary. 9 Experimental design in the presence of covariates. 9.1 Key concepts. 9.2 Case: the polypropylene experiment. 9.2.1 Problem and design. 9.2.2 Data analysis. 9.3 Peek into the black box. 9.3.1 Covariates or concomitant variables. 9.3.2 Models and design criteria in the presence of covariates. 9.3.3 Designs robust to time trends. 9.3.4 Design construction algorithms. 9.3.5 To randomize or not to randomize. 9.3.6 Final thoughts. 9.4 Background reading. 9.5 Summary. 10 A split-plot design. 10.1 Key concepts. 10.2 Case: the wind tunnel experiment. 10.2.1 Problem and design. 10.2.2 Data analysis. 10.3 Peek into the black box. 10.3.1 Split-plot terminology. 10.3.2 Model. 10.3.3 Inference from a split-plot design. 10.3.4 Disguises of a split-plot design. 10.3.5 Required number of whole plots and runs. 10.3.6 Optimal design of split-plot experiments. 10.3.7 A design construction algorithm for optimal split-plot designs. 10.3.8 Difficulties when analyzing data from split-plot experiments. 10.4 Background reading. 10.5 Summary. 11 A two-way split-plot design. 11.1 Key concepts. 11.2 Case: the battery cell experiment. 11.2.1 Problem and design. 11.2.2 Data analysis. 11.3 Peek into the black box. 11.3.1 The two-way split-plot model. 11.3.2 Generalized least squares estimation. 11.3.3 Optimal design of two-way split-plot experiments. 11.3.4 A design construction algorithm for D-optimal two-way split-plot designs. 11.3.5 Extensions and related designs. 11.4 Background reading. 11.5 Summary. Bibliography. Index.

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Book SynopsisThe quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning.Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications.Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class.

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Book SynopsisIntroductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields. There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems. Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization. Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, such as greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer. Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.Trade Review“This book introduces combinatorial optimization with a methodology-oriented organization. It targets undergraduate and graduate students and contains a good mix of theoretical results (with proof) and examples, which helps the reader acquire ideas and concepts. The chapters end with a list of exercises for the students.” (Francisco Chicano, Mathematical Reviews, January, 2024)“The book can appropriately be used as a textbook in a graduate course. All the algorithms are clearly explained and presented. It is a very valuable book for successful application of real problems from combinatorial optimization. … this book is an excellent contribution to the field of combinatorial optimization, and it is highly recommended to the students and researchers in optimization.” (Samir Kumar Neogy, zbMATH 1512.90001, 2023)Table of Contents1. Introduction.-2. Divide-and-Conquer.- 3. Dynamic Programming and Shortest Path.- 4. Greedy Algorithm and Spanning Tree.- 5. Incremental Method and Maximum Network Flow.- 6. Linear Programming.- 7. Primal-Dual Methods and Minimum Cost Flow.- 8. NP-hard Problems and Approximation Algorithms.- 9. Restriction and Steiner Tree.- 10. Greedy Approximation and Submodular Optimization.- 11. Relaxation and Rounding. 12. Nonsubmodular Optimization.- Bibliography.

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Book SynopsisThis is a graduate-level introduction to the key ideas and theoretical foundation of the vibrant field of optimal mass transport in the Euclidean setting. Taking a pedagogical approach, it introduces concepts gradually and in an accessible way, while also remaining technically and conceptually complete.Trade Review'Francesco Maggi's book is a detailed and extremely well written explanation of the fascinating theory of Monge-Kantorovich optimal mass transfer. I especially recommend Part IV's discussion of the 'linear' cost problem and its subtle mathematical resolution.' Lawrence C. Evans, University of California, Berkeley'Over the last three decades, optimal transport has revolutionized the mathematical analysis of inequalities, differential equations, dynamical systems, and their applications to physics, economics, and computer science. By exposing the interplay between the discrete and Euclidean settings, Maggi's book makes this development uniquely accessible to advanced undergraduates and mathematical researchers with a minimum of prerequisites. It includes the first textbook accounts of the localization technique known as needle decomposition and its solution to Monge's centuries old cutting and filling problem (1781). This book will be an indispensable tool for advanced undergraduates and mathematical researchers alike.' Robert McCann, University of TorontoTable of ContentsPreface; Notation; Part I. The Kantorovich Problem: 1. An introduction to the Monge problem; 2. Discrete transport problems; 3. The Kantorovich problem; Part II. Solution of the Monge Problem with Quadratic Cost: the Brenier-McCann Theorem: 4. The Brenier theorem; 5. First order differentiability of convex functions; 6. The Brenier-McCann theorem; 7. Second order differentiability of convex functions; 8. The Monge-Ampère equation for Brenier maps; Part III. Applications to PDE and the Calculus of Variations and the Wasserstein Space: 9. Isoperimetric and Sobolev inequalities in sharp form; 10. Displacement convexity and equilibrium of gases; 11. The Wasserstein distance W2 on P2(Rn); 12. Gradient flows and the minimizing movements scheme; 13. The Fokker-Planck equation in the Wasserstein space; 14. The Euler equations and isochoric projections; 15. Action minimization, Eulerian velocities and Otto's calculus; Part IV. Solution of the Monge Problem with Linear Cost: the Sudakov Theorem: 16. Optimal transport maps on the real line; 17. Disintegration; 18. Solution to the Monge problem with linear cost; 19. An introduction to the needle decomposition method; Appendix A: Radon measures on Rn and related topics; Appendix B: Bibliographical Notes; Bibliography; Index.

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Book SynopsisInteger linear programming (ILP) is a versatile modeling and optimization technique that is increasingly used in non-traditional ways in biology, with the potential to transform biological computation. However, few biologists know about it. This how-to and why-do text introduces ILP through the lens of computational and systems biology. It uses in-depth examples from genomics, phylogenetics, RNA, protein folding, network analysis, cancer, ecology, co-evolution, DNA sequencing, sequence analysis, pedigree and sibling inference, haplotyping, and more, to establish the power of ILP. This book aims to teach the logic of modeling and solving problems with ILP, and to teach the practical ''work flow'' involved in using ILP in biology. Written for a wide audience, with no biological or computational prerequisites, this book is appropriate for entry-level and advanced courses aimed at biological and computational students, and as a source for specialists. Numerous exercises and accompanying soTrade Review'In his classic accessible teaching style, Gusfield teaches us why integer linear programming (ILP) is the most useful mathematical idea you've probably never heard of. Read this book to learn how what you don't know can hurt you, and why ILP should be your new favorite method.' Trey Ideker, University of California, San Diego'Once again, Dan Gusfield has written an accessible book that shows that algorithmic rigor need not be sacrificed when solving real-world problems. He explains integer linear programming in the context of real-world biology. In doing so, the reader has an enriched understanding of both algorithmic details and the challenges in modern biology.' Russ Altman, Stanford University, CaliforniaTable of ContentsPreface; Part I: 1. A fly-over introduction; 2. Biological networks and graphs; 3. Character compatibility; 4. Near-cliques; 5. Parsimony in phylogenetics; 6. RNA folding; 7. Protein problems; 8. Tanglegrams; 9. TSP in genomics; 10. Molecular sequence analysis; 11. Metabolic networks and engineering; 12. ILP idioms; Part II: 13. Communities and cuts; 14. Corrupted data and extensions in phylogenetics; 15. More tanglegrams and trees; 16. Return to Steiner-trees; 17. Exploiting protein networks; 18. More strings and sequences; 19. Max-likelihood pedigrees; 20. Haplotyping; 21. Extended exercises; 22. What's next?; Epilogue: opinionated comments.

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Book Synopsis Provides well-written self-contained chapters, including problem sets and exercises, making it ideal for the classroom setting; Introduces applied optimization to the hazardous waste blending problem; Explores linear programming, nonlinear programming, discrete optimization, global optimization, optimization under uncertainty, multi-objective optimization, optimal control and stochastic optimal control; Includes an extensive bibliography at the end of each chapter and an index; GAMS files of case studies for Chapters 2, 3, 4, 5, and 7 are linked to http://www.springer.com/math/book/978-0-387-76634-8; Solutions manual available upon adoptions.Table of Contents1. Introduction.- 2. Linear Programming.- 3. Nonlinear Programming.-4. Discrete Optimization.- 5. Optimization Under Uncertainty.- 6. Multiobjective Optimization.- 7.Optimal Control and Dynamic Optimization.- Index.

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Book SynopsisReliability and maintenance modeling with optimization is the most fundamental and interdisciplinary research area that can be applied to every technical and management field. Reliability and Maintenance Modeling with Optimization: Advances and Applications aims at providing the most recent advances and achievements in reliability and maintenance.The book discusses replacement, repair, and inspection, offers estimation and statistical tests, covers accelerated life testing, explores warranty analysis manufacturing, and includes service reliability.The targeted readers are researchers interested in reliability and maintenance engineering. The book can serve as supplemental reading in professional seminars for engineers, designers, project managers, and graduate students.Table of Contents1. Nine Memorial Research Works. 2. Replacement First and Last Policies with Random Times for Redundant Systems. 3. Backup Policies with Random Data Updates. 4. An Optimal Age Replacement Policy for a Reparable System Consisting of Main and Auxiliary Subsystems. 5. Extended replacement policy in damage models. 6. Optimal Checking Policy for a Server System with Cyber Attack. 7. Reliability Analysis of Congestion Control Scheme with Code Error Correction Methods. 8. The Optimal Design of Consecutive-k Systems. 9. Optimal Social Infrastructure Maintenance Models. 10. Optimal Maintenance Problem with OSS-Oriented EVM for OSS Project. 11. Reliability Assessment Model Based on Wiener Process Considering Network Environment for Edge Computing. 12. Approximated Estimation of Software Target Failure Measures Conforming IEC 61508. 13. Phase-Type Expansion of Markov Regenerative Processes and Its Application to Reliability Problems. 14. A Hybrid Model Fitting Framework considering Accuracy and Performance. 15. Alternating α-Series Process. 16. Optimum Staggered Testing Strategy for Redundant Safety Instrumented Systems with Different Testing Intervals. 17. Modules Of Multi-State Systems - Introduction To Three Modules Theorem. 18. A postponed repair model for a mission-based system based on a three-stage failure process.

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Book Synopsis1 Introduction to Lie Groups.- 1.1. Manifolds.- 1.2. Lie Groups.- 1.3. Vector Fields.- 1.4. Lie Algebras.- 1.5. Differential Forms.- Notes.- Exercises.- 2 Symmetry Groups of Differential Equations.- 2.1. Symmetries of Algebraic Equations.- 2.2. Groups and Differential Equations.- 2.3. Prolongation.- 2.4. Calculation of Symmetry Groups.- 2.5. Integration of Ordinary Differential Equations.- 2.6. Nondegeneracy Conditions for Differential Equations.- Notes.- Exercises.- 3 Group-Invariant Solutions.- 3.1. Construction of Group-Invariant Solutions.- 3.2. Examples of Group-Invariant Solutions.- 3.3. Classification of Group-Invariant Solutions.- 3.4. Quotient Manifolds.- 3.5. Group-Invariant Prolongations and Reduction.- Notes.- Exercises.- 4 Symmetry Groups and Conservation Laws.- 4.1. The Calculus of Variations.- 4.2. Variational Symmetries.- 4.3. Conservation Laws.- 4.4. Noether's Theorem.- Notes.- Exercises.- 5 Generalized Symmetries.- 5.1. Generalized Symmetries of Differential Equations.- 5.2. Récursion Operators, Master Symmetries and Formal Symmetries.- 5.3. Generalized Symmetries and Conservation Laws.- 5.4. The Variational Complex.- Notes.- Exercises.- 6 Finite-Dimensional Hamiltonian Systems.- 6.1. Poisson Brackets.- 6.2. Symplectic Structures and Foliations.- 6.3. Symmetries, First Integrals and Reduction of Order.- Notes.- Exercises.- 7 Hamiltonian Methods for Evolution Equations.- 7.1. Poisson Brackets.- 7.2. Symmetries and Conservation Laws.- 7.3. Bi-Hamiltonian Systems.- Notes.- Exercises.- References.- Symbol Index.- Author Index.Table of Contents1 Introduction to Lie Groups.- 1.1. Manifolds.- Change of Coordinates.- Maps Between Manifolds.- The Maximal Rank Condition.- Submanifolds.- Regular Submanifolds.- Implicit Submanifolds.- Curves and Connectedness.- 1.2. Lie Groups.- Lie Subgroups.- Local Lie Groups.- Local Transformation Groups.- Orbits.- 1.3. Vector Fields.- Flows.- Action on Functions.- Differentials.- Lie Brackets.- Tangent Spaces and Vectors Fields on Submanifolds.- Frobenius’ Theorem.- 1.4. Lie Algebras.- One-Parameter Subgroups.- Subalgebras.- The Exponential Map.- Lie Algebras of Local Lie Groups.- Structure Constants.- Commutator Tables.- Infinitesimal Group Actions.- 1.5. Differential Forms.- Pull-Back and Change of Coordinates.- Interior Products.- The Differential.- The de Rham Complex.- Lie Derivatives.- Homotopy Operators.- Integration and Stokes’ Theorem.- Notes.- Exercises.- 2 Symmetry Groups of Differential Equations.- 2.1. Symmetries of Algebraic Equations.- Invariant Subsets.- Invariant Functions.- Infinitesimal Invariance.- Local Invariance.- Invariants and Functional Dependence.- Methods for Constructing Invariants.- 2.2. Groups and Differential Equations.- 2.3. Prolongation.- Systems of Differential Equations.- Prolongation of Group Actions.- Invariance of Differential Equations.- Prolongation of Vector Fields.- Infinitesimal Invariance.- The Prolongation Formula.- Total Derivatives.- The General Prolongation Formula.- Properties of Prolonged Vector Fields.- Characteristics of Symmetries.- 2.4. Calculation of Symmetry Groups.- 2.5. Integration of Ordinary Differential Equations.- First Order Equations.- Higher Order Equations.- Differential Invariants.- Multi-parameter Symmetry Groups.- Solvable Groups.- Systems of Ordinary Differential Equations.- 2.6. Nondegeneracy Conditions for Differential Equations.- Local Solvability.- In variance Criteria.- The Cauchy—Kovalevskaya Theorem.- Characteristics.- Normal Systems.- Prolongation of Differential Equations.- Notes.- Exercises.- 3 Group-Invariant Solutions.- 3.1. Construction of Group-Invariant Solutions.- 3.2. Examples of Group-Invariant Solutions.- 3.3. Classification of Group-Invariant Solutions.- The Adjoint Representation.- Classification of Subgroups and Subalgebras.- Classification of Group-Invariant Solutions.- 3.4. Quotient Manifolds.- Dimensional Analysis.- 3.5. Group-Invariant Prolongations and Reduction.- Extended Jet Bundles.- Differential Equations.- Group Actions.- The Invariant Jet Space.- Connection with the Quotient Manifold.- The Reduced Equation.- Local Coordinates.- Notes.- Exercises.- 4 Symmetry Groups and Conservation Laws.- 4.1. The Calculus of Variations.- The Variational Derivative.- Null Lagrangians and Divergences.- Invariance of the Euler Operator.- 4.2. Variational Symmetries.- Infinitesimal Criterion of Invariance.- Symmetries of the Euler—Lagrange Equations.- Reduction of Order.- 4.3. Conservation Laws.- Trivial Conservation Laws.- Characteristics of Conservation Laws.- 4.4. Noether’s Theorem.- Divergence Symmetries.- Notes.- Exercises.- 5 Generalized Symmetries.- 5.1. Generalized Symmetries of Differential Equations.- Differential Functions.- Generalized Vector Fields.- Evolutionary Vector Fields.- Equivalence and Trivial Symmetries.- Computation of Generalized Symmetries.- Group Transformations.- Symmetries and Prolongations.- The Lie Bracket.- Evolution Equations.- 5.2. Récursion Operators, Master Symmetries and Formal Symmetries.- Frechet Derivatives.- Lie Derivatives of Differential Operators.- Criteria for Recursion Operators.- The Korteweg—de Vries Equation.- Master Symmetries.- Pseudo-differential Operators.- Formal Symmetries.- 5.3. Generalized Symmetries and Conservation Laws.- Adjoints of Differential Operators.- Characteristics of Conservation Laws.- Variational Symmetries.- Group Transformations.- Noether’s Theorem.- Self-adjoint Linear Systems.- Action of Symmetries on Conservation Laws.- Abnormal Systems and Noether’s Second Theorem.- Formal Symmetries and Conservation Laws.- 5.4. The Variational Complex.- The D-Complex.- Vertical Forms.- Total Derivatives of Vertical Forms.- Functionals and Functional Forms.- The Variational Differential.- Higher Euler Operators.- The Total Homotopy Operator.- Notes.- Exercises.- 6 Finite-Dimensional Hamiltonian Systems.- 6.1. Poisson Brackets.- Hamiltonian Vector Fields.- The Structure Functions.- The Lie-Poisson Structure.- 6.2. Symplectic Structures and Foliations.- The Correspondence Between One-Forms and Vector Fields.- Rank of a Poisson Structure.- Symplectic Manifolds.- Maps Between Poisson Manifolds.- Poisson Submanifolds.- Darboux’ Theorem.- The Co-adjoint Representation.- 6.3. Symmetries, First Integrals and Reduction of Order.- First Integrals.- Hamiltonian Symmetry Groups.- Reduction of Order in Hamiltonian Systems.- Reduction Using Multi-parameter Groups.- Hamiltonian Transformation Groups.- The Momentum Map.- Notes.- Exercises.- 7 Hamiltonian Methods for Evolution Equations.- 7.1. Poisson Brackets.- The Jacobi Identity.- Functional Multi-vectors.- 7.2. Symmetries and Conservation Laws.- Distinguished Functionals.- Lie Brackets.- Conservation Laws.- 7.3. Bi-Hamiltonian Systems.- Recursion Operators.- Notes.- Exercises.- References.- Symbol Index.- Author Index.

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Book SynopsisPresenting a fresh look at process control, this new text demonstrates state-space approach shown in parallel with the traditional approach to explain the strategies used in industry today. Modern time-domain and traditional transform-domain methods are integrated throughout and explain the advantages and limitations of each approach; the fundamental theoretical concepts and methods of process control are applied to practical problems. To ensure understanding of the mathematical calculations involved, MATLAB is included for numeric calculations and MAPLE for symbolic calculations, with the math behind every method carefully explained so that students develop a clear understanding of how and why the software tools work. Written for a one-semester course with optional advanced-level material, features include solved examples, cases that include a number of chemical reactor examples, chapter summaries, key terms, and concepts, as well as over 240 end-of-chapter problems, focused computatiTrade Review'Provides a fresh perspective through the integrated coverage of modern state-space and traditional transfer function approaches. The mathematical derivations are detailed and accessible, aiding clear understanding of the basic as well as the more advanced topics.' Prodromos Daoutidis, University of Minnesota'Breaking new ground in the crowded field of process control textbooks, this book provides the foundation for teaching a modern undergraduate process control course in the twenty-first century. It is exceptionally well written and organized, and includes numerous examples, making it a must-have for all process control researchers, students and engineers.' Panagiotis D. Christofides, University of California, Los AngelesTable of ContentsContents; Preface; 1. Introduction; 2. Dynamic Models for Chemical Process Systems; 3. First Order Systems; 4. Connections of First Order Systems; 5. Second Order Systems; 6. Linear Higher Order Systems; 7. Eigenvalue Analysis – Asymptotic Stability; 8. Transfer Function Analysis of the Input/Output Behavior; 9. Frequency Response; 10. The Feedback Control System; 11. Block Diagram Reduction and Transient Response Calculation in a Feedback Control System; 12. Steady-State and Stability Analysis of the Closed Loop System; 13. State Space Description and Analysis of the Closed Loop System; 14. Systems with Dead Time; 15. Parametric Analysis of Closed Loop Dynamics – Root Locus Diagrams; 16. Optimal Selection of Controller Parameters; 17. Bode and Nyquist Stability Criteria – Gain and Phase Margins; 18. Multiple-Input-Multiple-Output Systems; 19. Synthesis of Model-Based Feedback Controllers; 20. Cascade, Ratio and Feedforward Control; Appendix A; Appendix B.

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Book SynopsisIn the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself.Trade Review'The field of mathematical programming has two major themes: linear programming and convex programming. The far-reaching impact of the first theory in computer science, game theory and engineering is well known. We are now witnessing the growth of the second theory as it finds its way into diverse fields such as machine learning, mathematical economics and quantum computing. This much-awaited book with its unique approach, steeped in the modern theory of algorithms, will go a long way in making this happen.' Vijay V. Vazirani, Distinguished Professor at University of California, Irvine'I had thought that there is no need for new books about convex optimization but this book proves me wrong. It treats both classic and cutting-edge topics with an unparalleled mix of clarity and rigor, building intuitions about key ideas and algorithms driving the field. A must read for anyone interested in optimization!' Aleksander Madry, Massachusetts Institute of Technology'Vishnoi's book provides an exceptionally good introduction to convex optimization for students and researchers in computer science, operations research, and discrete optimization. The book gives a comprehensive introduction to classical results as well as to some of the most recent developments. Concepts and ideas are introduced from first principles, conveying helpful intuitions. There is significant emphasis on bridging continuous and discrete optimization, in particular, on recent breakthroughs on flow problems using convex optimization methods; the book starts with an enlightening overview of the interplay between these areas.' László Végh, LSE'Recommended.' M. Bona, Choice ConnectTable of Contents1. Bridging continuous and discrete optimization; 2. Preliminaries; 3. Convexity; 4. Convex optimization and efficiency; 5. Duality and optimality; 6. Gradient descent; 7. Mirror descent and multiplicative weights update; 8. Accelerated gradient descent; 9. Newton's method; 10. An interior point method for linear programming; 11. Variants of the interior point method and self-concordance; 12. Ellipsoid method for linear programming; 13. Ellipsoid method for convex optimization.

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Book SynopsisBased on the author''s forty years of teaching experience, this unique textbook covers both basic and advanced concepts of optimization theory and methods for process systems engineers. Topics covered include continuous, discrete and logic optimization (linear, nonlinear, mixed-integer and generalized disjunctive programming), optimization under uncertainty (stochastic programming and flexibility analysis), and decomposition techniques (Lagrangean and Benders decomposition). Assuming only a basic background in calculus and linear algebra, it enables easy understanding of mathematical reasoning, and numerous examples throughout illustrate key concepts and algorithms. End-of-chapter exercises involving theoretical derivations and small numerical problems, as well as in modeling systems like GAMS, enhance understanding and help put knowledge into practice. Accompanied by two appendices containing web links to modeling systems and models related to applications in PSE, this is an essentialTrade Review'Authored by Ignacio Grossmann, the creator and key developer of the field of mixed integer nonlinear programming, this outstanding textbook provides a thorough and comprehensive treatment of fundamental concepts, optimization models and effective solution strategies for discrete and continuous optimization. It is an essential, 'must-have' reference for all students, researchers and practitioners in process systems engineering.' Lorenz Biegler, Carnegie Mellon University'From the globally recognized leading authority in the field of process systems engineering, this long-awaited book will definitely become the standard reference for anyone interested in optimization. It is very well thought and written, with excellent presentation of the material. The theory is described in a very effective, rigorous, and clear way, with appropriate explanations and examples used throughout, covering traditional topics such as linear and nonlinear optimization concepts and mixed-integer linear programming, along with more advanced topics, such as disjunctive programming, global optimization, and stochastic programming. A real gem and a must read!' Stratos Pistikopoulos, Texas A & M University'Excellent coverage of the basic concepts and approaches developed in the area of process systems engineering in the last forty years. A unique book that can be easily adapted to advanced undergraduate and graduate-level classes to provide overall guidance to different tools that can be used to model and optimize complex engineering problems. I am certainly looking forward to using it in my class on mathematical modeling and optimization principles.' Marianthi Ierapetritou, University of DelawareTable of ContentsPreface; 1. Optimization in process systems engineering; 2. Solving nonlinear equations; 3. Basic theoretical concepts in optimization; 4. Nonlinear programming algorithms; 5. Linear programming; 6. Mixed-integer programming models; 7. Systematic modeling of constraints with logic; 8. Mixed-integer linear programming; 9 Mixed-integer nonlinear programming; 10. Generalized disjunctive programming; 11. Constraint programming; 12. Nonconvex optimization; 13. Lagrangean decomposition; 14. Stochastic programming; 15. Flexibility analysis; Appendix A. Modeling systems and optimization software; Appendix B. Optimization models for process systems engineering; References; Index.

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Book SynopsisUsing a pedagogical, unified approach, this book presents both the analytic and combinatorial aspects of convexity and its applications in optimization. On the structural side, this is done via an exposition of classical convex analysis and geometry, along with polyhedral theory and geometry of numbers. On the algorithmic/optimization side, this is done by the first ever exposition of the theory of general mixed-integer convex optimization in a textbook setting. Classical continuous convex optimization and pure integer convex optimization are presented as special cases, without compromising on the depth of either of these areas. For this purpose, several new developments from the past decade are presented for the first time outside technical research articles: discrete Helly numbers, new insights into sublinear functions, and best known bounds on the information and algorithmic complexity of mixed-integer convex optimization. Pedagogical explanations and more than 300 exercises make this book ideal for students and researchers.

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Book SynopsisThis book provides an essential introduction to Stochastic Programming, especially intended for graduate students. The book begins by exploring a linear programming problem with random parameters, representing a decision problem under uncertainty. Several models for this problem are presented, including the main ones used in Stochastic Programming: recourse models and chance constraint models. The book not only discusses the theoretical properties of these models and algorithms for solving them, but also explains the intrinsic differences between the models. In the book’s closing section, several case studies are presented, helping students apply the theory covered to practical problems. The book is based on lecture notes developed for an Econometrics and Operations Research course for master students at the University of Groningen, the Netherlands - the longest-standing Stochastic Programming course worldwide. Trade Review“The book is well written. The book will be of interest to mathematicians, engineers, economics and especially graduate students.” (I. M. Stancu-Minasian, zbMATH 1446.90118, 2020)Table of ContentsIntroduction.- Random Objective Functions.- Recourse Models.- Stochastic Mixed-integer Programming.- Chance Constraints.- Integrated Chance Constraints.- Assignments.- Case Studies.

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Book SynopsisThis richly illustrated book introduces the subject of optimization to a broad audience with a balanced treatment of theory, models and algorithms. Through numerous examples from statistical learning, operations research, engineering, finance and economics, the text explains how to formulate and justify models while accounting for real-world considerations such as data uncertainty. It goes beyond the classical topics of linear, nonlinear and convex programming and deals with nonconvex and nonsmooth problems as well as games, generalized equations and stochastic optimization.The book teaches theoretical aspects in the context of concrete problems, which makes it an accessible onramp to variational analysis, integral functions and approximation theory. More than 100 exercises and 200 fully developed examples illustrate the application of the concepts. Readers should have some foundation in differential calculus and linear algebra. Exposure to real analysis would be helpful but is not prerequisite. Trade Review“In the reviewer's opinion, this is an important book … . a lot of applications are given, so on one hand the readers can benefit from deep insights into the mathematical background of optimization theory … . This book, which as all books reflects the tastes of its authors, is a solid reference, not only for graduate students and postgraduate students, but also for all those researchers interested in recent developments of optimization theory and methods.” (Giorgio Giorgi, Mathematical Reviews, December, 2022)Table of ContentsPrelude.- Convex optimization.- Optimization under uncertainty.- Minimization problems.- Perturbation and duality.- Without convexity or smoothness.- Generalized Equations.- Risk modeling and sample averages.- Games and minsup problems.- Decomposition.

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Book SynopsisThis book introduces solutions for sports scheduling problems in a variety of settings. In particular the book covers timetabling, the traveling tournament problem, carryover minimization, breaks minimization, tournament design, tournament planning, and referee assignment. A rich selection of applications to sports such as football, baseball, basketball, cricket or hockey are employed to illustrate the methods and techniques. In a step-by-step tutorial format the book describes the use of graph theory concepts, local search operators and integer programming in the context of sports scheduling. The methods presented in this book are essential to sports scheduling in all its dimensions, from tournaments that are followed by millions of people across the world, with broadcast rights that amount to hundreds of millions of dollars in some competitions, to amateur leagues that require coordination and logistical efforts due to the large number of tournaments and competitors.Table of ContentsLeagues, tournaments, and schedules.- Combinatorial structures.- Metaheuristics and local search.- Integer programming approaches.- Case studies.

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Book Synopsis„Shape optimization and spectral theory” is a survey book aiming to give an overview of recent results in spectral geometry and its links with shape optimization. It covers most of the issues which are important for people working in PDE and differential geometry interested in sharp inequalities and qualitative behaviour for eigenvalues of the Laplacian with different kind of boundary conditions (Dirichlet, Robin and Steklov). This includes: existence of optimal shapes, their regularity, the case of special domains like triangles, isospectrality, quantitative form of the isoperimetric inequalities, optimal partitions, universal inequalities and numerical results. Much progress has been made in these extremum problems during the last ten years and this edited volume presents a valuable update to a wide community interested in these topics. List of contributors Antunes Pedro R.S., Ashbaugh Mark, Bonnaillie-Noël Virginie, Brasco Lorenzo, Bucur Dorin, Buttazzo Giuseppe, De Philippis Guido, Freitas Pedro, Girouard Alexandre, Helffer Bernard, Kennedy James, Lamboley Jimmy, Laugesen Richard S., Oudet Edouard, Pierre Michel, Polterovich Iosif, Siudeja Bartłomiej A., Velichkov Bozhidar

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Book SynopsisThis text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favorite problems to understand their strengths and weaknesses, also making the text suitable for a self-study.Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation and numerous application areas in science and engineering. This text is designed as an introduction to UQ for senior undergraduate and graduate students with a mathematical or statistical background and also for researchers from the mathematical sciences or from applications areas who are interested in the field.T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.Trade Review“Book is one of very few that discuss a vast array of topics in the developing field of uncertainty quantification (UQ). … The text is mathematically rigorous, and though the intended audience is the senior undergraduate or early graduate mathematics student … . this is a book I might recommend to students as a reference for topics related to UQ ... . Overall, this introduction to UQ leaves something to be desired. It is well written … .” (Talea L. Mayo, SIAM Review, Vol. 59 (1), March, 2017)“This book presents a collection of mathematical results related to Uncertainly Quantification (UQ). It is intended as a textbook for senior undergraduate or graduate students with a background in mathematics and statistics. … The book might be suitable for a research seminar where students are exposed for the first time to the mathematics behind UQ.” (Elisabeth Ullmann, Mathematical Reviews, February, 2017)“This book aims to provide an introduction to the mathematics of the quantification of uncertainty. It is intended for students in mathematics and statistics. In the US this would be a graduate level textbook.” (William J. Satzer, MAA Reviews, maa.org, February, 2016)Table of ContentsIntroduction.- Measure and Probability Theory.- Banach and Hilbert Spaces.- Optimization Theory.- Measures of Information and Uncertainty.- Bayesian Inverse Problems.- Filtering and Data Assimilation.- Orthogonal Polynomials and Applications.- Numerical Integration.- Sensitivity Analysis and Model Reduction.- Spectral Expansions.- Stochastic Galerkin Methods.- Non-Intrusive Methods.- Distributional Uncertainty.- References.- Index.

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Book SynopsisThis book treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. The author describes and analyses some of the best-known algorithms for colouring arbitrary graphs, focusing on whether these heuristics can provide optimal solutions in some cases; how they perform on graphs where the chromatic number is unknown; and whether they can produce better solutions than other algorithms for certain types of graphs, and why. The introductory chapters explain graph colouring, and bounds and constructive algorithms. The author then shows how advanced, modern techniques can be applied to classic real-world operational research problems such as seating plans, sports scheduling, and university timetabling. He includes many examples, suggestions for further reading, and historical notes, and the book is supplemented by a website with an online suite of downloadable code. The book will be of value to researchers, graduate students, and practitioners in the areas of operations research, theoretical computer science, optimization, and computational intelligence. The reader should have elementary knowledge of sets, matrices, and enumerative combinatorics.Trade Review“The book gives a comprehensive description and handling on arguably one of the most important notions of combinatorics—graph coloring. … The book is nicely written, and carries a big pile of information valuable for both users and researchers in the field.” (András Sándor Pluhár, Mathematical Reviews, February, 2017)“This well-written book will serve as a utilitarian guide to graph coloring and its practical applications. It includes many definitions, theorems, proofs, algorithms, and pointers for further reading. The book will be helpful for teaching courses on graph coloring to students of mathematics and computer science. I strongly recommend it for the intended audience.” (S. V. Nagaraj, Computing Reviews, computingreviews.com, June, 2016)“The book is a comprehensive guide to graph colouring algorithms. … The book is a nice textbook for both undergraduate and graduate students in the areas of operations research and theoretical computer science. … Finally, it is a good source of knowledge for practitioners.” (Marcin Anholcer, zbMATH 1330.05002, 2016)Table of ContentsIntroduction to Graph Colouring.- Bounds and Constructive Algorithms.- Advanced Techniques for Graph Colouring.- Algorithm Case Studies.- Applications and Extensions.- Designing Seating Plans.- Designing Sports Leagues.- Designing University Timetables.- App. A, Computing Resources.- References.- Index.

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Book SynopsisCollating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.Table of ContentsPreface.- Bernard Dacorogna: The pullback equation.- Nicola Fusco: The stability of the isoperimetric inequality.- Stefan Müller: Mathematical problems in thin elastic sheets: scaling limits.-packing, crumpling and singularities.- Vladimir Sverák: Aspects of PDEs related to Fluid Flows.

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Book SynopsisThis book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.Table of ContentsAlberto Farina and Enrico Valdinoci:Introduction.-Alessio Figalli:Global Existence for the Semi-Geostrophic Equations via Sobolev Estimates for Monge-Ampère.-Ireneo Peral Alonso: On Some Elliptic and Parabolic Equations Related to Growth Models.- Enrico Valdinoci: All Functions are (locally) S-harmonic (up to a small error) – and Applications

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Book SynopsisThe authors stress the relative simplicity, efficiency, flexibility of use, and suitability of various approaches used to solve difficult optimization problems. The authors are experienced, interdisciplinary lecturers and researchers and in their explanations they demonstrate many shared foundational concepts among the key methodologies. This textbook is a suitable introduction for undergraduate and graduate students, researchers, and professionals in computer science, engineering, and logistics.Trade Review“I would recommend this book for students in the area of operations research, but also for students and professionals from other fields (like natural sciences or social sciences) who would like not only to apply metaheuristics to solve the problems … but also to understand how they work.” (Marcin Anholcer, zbMATH 1427.90001, 2020)Table of ContentsProblems, Algorithms, Computational Complexity.- Search Space.- Tabu Search.- Simulated Annealing.- Ant Colony Optimization (ACO).- Non-PSO Optimization.- Firefly Algorithm, Cuckoo Algorithm, Lévy Flights.- Evolutionary Algorithms: Foundations.- Evolutionary Algorithms: Advanced.- Phase Transition in Optimization Problems.- Performance and Limitations of Metaheuristics.- Statistical Analysis of Research Spaces.

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Book SynopsisFrom the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"Trade ReviewFrom the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books. . . [is] that they are designed not for the expert, but for those who wish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"Table of ContentsIX. Inner Construction of the Subdifferential.- X. Conjugacy in Convex Analysis.- XI. Approximate Subdifferentials of Convex Functions.- XII. Abstract Duality for Practitioners.- XIII. Methods of ?-Descent.- XIV. Dynamic Construction of Approximate Subdifferentials: Dual Form of Bundle Methods.- XV. Acceleration of the Cutting-Plane Algorithm: Primal Forms of Bundle Methods.- Bibliographical Comments.- References.

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Book SynopsisSince Additive Manufacturing (AM) techniques allow the manufacture of complex-shaped structures the combination of lightweight construction, topology optimization, and AM is of significant interest. Besides the established continuum topology optimization methods, less attention is paid to algorithm-driven optimization based on linear optimization, which can also be used for topology optimization of truss-like structures.To overcome this shortcoming, we combined linear optimization, Computer-Aided Design (CAD), numerical shape optimization, and numerical simulation into an algorithm-driven product design process for additively manufactured truss-like structures. With our Ansys SpaceClaim add-in construcTOR, which is capable of obtaining ready-for-machine-interpretation CAD data of truss-like structures out of raw mathematical optimization data, the high performance of (heuristic-based) optimization algorithms implemented in linear programming software is now available to the CAD community.Table of ContentsIntroduction.- Physical and Technical Background.- Optimization of Truss Structures.- Bridging Algorithm-Driven Truss Optimization and Additive Manufacturing.- Mixed-Integer Linear Programming for Truss Optimization.- CAD-Based Mathematical Optimization.- Computational Study.- Conclusion and Outlook.

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Book SynopsisThese lecture notes are devoted to the analysis of a nonlocal equation in the whole of Euclidean space. In studying this equation, all the necessary material is introduced in the most self-contained way possible, giving precise references to the literature when necessary. The results presented are original, but no particular prerequisite or knowledge of the previous literature is needed to read this text. The work is accessible to a wide audience and can also serve as introductory research material on the topic of nonlocal nonlinear equations.Table of ContentsIntroduction.- The problem studied in this monograph.- Functional analytical setting.- Existence of a minimal solution and proof of Theorem 2.2.2.- Regularity and positivity of the solution.- Existence of a second solution and proof of Theorem 2.2.4.

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Book SynopsisThis book discusses comprehensively the advanced manufacturing processes, including illustrative examples of the processes, mathematical modeling, and the need to optimize associated parameter problems. In addition, it describes in detail the cohort intelligence methodology and its variants along with illustrations, to help readers gain a better understanding of the framework. The theoretical and statistical rigor is validated by comparing the solutions with evolutionary algorithms, simulation annealing, response surface methodology, the firefly algorithm, and experimental work. Lastly, the book critically reviews several socio-inspired optimization methods. Table of ContentsIntroduction.- A Brief Review of Socio-Inspired Metaheuristics.- Multi Cohort Intelligence Algorithm.- Optimization of Electric Discharge Machining (EDM).- Optimization of Abrasive Water Jet Machining (AWJM).- Optimization of Micro Milling Process.- Optimization of Micro Drilling Process.- Optimization of Cutting Forces in Micro Drilling of CFRP Composites for Aerospace Applications.- Optimization of Micro Turning Process.- Optimization of Machining Process Parameters of Titanium Alloy Under (MQL) Environment.

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Book SynopsisThis monograph represents a historic breakthrough in the field of linear programming (LP)since George Dantzig first discovered the simplex method in 1947. Being both thoughtful and informative, it focuses on reflecting and promoting the state of the art by highlighting new achievements in LP. This new edition is organized in two volumes. The first volume addresses foundations of LP, including the geometry of feasible region, the simplex method and its implementation, duality and the dual simplex method, the primal-dual simplex method, sensitivity analysis and parametric LP, the generalized simplex method, the decomposition method, the interior-point method and integer LP method. The second volume mainly introduces contributions of the author himself, such as efficient primal/dual pivot rules, primal/dual Phase-I methods, reduced/D-reduced simplex methods, the generalized reduced simplex method, primal/dual deficient-basis methods, primal/dual face methods, a new decomposition principle, etc.Many important improvements were made in this edition. The first volume includes new results, such as the mixed two-phase simplex algorithm, dual elimination, fresh pricing scheme for reduced cost, bilevel LP models and intercepting of optimal solution set. In particular, the chapter Integer LP Method was rewritten with great gains of the objective cutting for new ILP solvers {\it controlled-cutting/branch} methods, as well as with an attractive implementation of the controlled-branch method. In the second volume, the `simplex feasible-point algorithm' was rewritten, and removed from the chapter Pivotal Interior-Point Method to form an independent chapter with the new title `Simplex Interior-Point Method', as it represents a class of efficient interior-point algorithms transformed from traditional simplex algorithms. The title of the original chapter was then changed to `Facial Interior-Point Method', as the remaining algorithms represent another class of efficient interior-point algorithms transformed from normal interior-point algorithms. Without exploiting sparsity, the original primal/dual face methods were implemented using Cholesky factorization. In order to deal with sparse computation, two new chapters discussing LU factorization were added to the second volume. The most exciting improvement came from the rediscovery of the reduced simplex method. In the first edition, the derivation of its prototype was presented in a chapter with the same title, and then converted into the so-called `improved' version in another chapter. Fortunately, the author recently found a quite concise new derivation, so he can now introduce the distinctive fresh simplex method in a single chapter. It is exciting that the reduced simplex method can be expected to be the best LP solver ever.With a focus on computation, the current edition contains many novel ideas, theories and methods, supported by solid numerical results. Being clear and succinct, its content reveals in a fresh manner, from simple to profound. In particular, a larger number of examples were worked out to demonstrate algorithms. This book is a rare work in LP and an indispensable tool for undergraduate and graduate students, teachers, practitioners, and researchers in LP and related fields.Table of ContentsChapter 1. Introduction.- Chapter 2. Geometry of Feasible Region.- Chapter 3. Simplex Method.- Chapter 4. Implementation of Simplex Method.- Chapter 5. Duality Principle and Dual Simplex Method.- Chapter 6. Primal-Dual Simplex Method.- Chapter 7. Sensitivity Analysis and Parametric LP.- Chapter 8. Generalized Simplex Method.- Chapter 9. Decomposition Method.- Chapter 10. Interior-Point Method.- Chapter 11. Integer Linear Programming (ILP).- Chapter 12. Pivot Rule.- Chapter 13. Dual Pivot Rule.- Chapter 14. Simplex Phase-I Method.- Chapter 15. Dual Simplex Phase-l Method.- Chapter 16. Reduced Simplex Method.- Chapter 17. D-Reduced Simplex Method.- Chapter 18. Generalized Reduced Simplex Method.- Chapter 19. Deficient-Basis Method.- Chapter 20. Dual Decient-Basis Method.- Chapter 21. Face Method with Cholesky Factorization.- Chapter 22. Dual Face Method with Cholesky Factorization.- Chapter 23. Face Method with LU Factorization.- Chapter 24. Dual Face Method with LU Factorization.- Chapter 25. Simplex Interior-Point Method.- Chapter 26. Facial Interior-Point Method.- Chapter 27. Decomposition Principle.

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Book SynopsisThe book focuses on Pareto optimality in cooperative games. Most of the existing works focus on the Pareto optimality of deterministic continuous-time systems or for the regular convex LQ case. To expand on the available literature, we explore the existence conditions of Pareto solutions in stochastic differential game for more general cases. In addition, the LQ Pareto game for stochastic singular systems, Pareto-based guaranteed cost control for uncertain mean-field stochastic systems, and the existence conditions of Pareto solutions in cooperative difference game are also studied in detail. Addressing Pareto optimality for more general cases and wider systems is one of the major features of the book, making it particularly suitable for readers who are interested in multi-objective optimal control. Accordingly, it offers a valuable asset for researchers, engineers, and graduate students in the fields of control theory and control engineering, economics, management science, mathematics, etc.Trade Review“The book provides a concise, clear summary of its subject matter. It will be a valuable reference for researchers looking to apply models of cooperative dynamic games in their work.” (Thomas Wiseman, zbMATH 1519.91003, 2023)Table of ContentsIntroduction.- Existence conditions of Pareto solutions in the finite horizon stochastic differential game.- Existence conditions of Pareto solutions in the infinite horizon stochastic differential game.- LQ Pareto game of the stochastic singular systems in finite horizon.- LQ Pareto game of the stochastic singular systems in infinite horizon.- Pareto-based guaranteed cost control of the uncertain mean-field stochastic systems.- Existence conditions of Pareto solutions in the finite horizon cooperative difference game.- Existence conditions of Pareto solutions in the infinite horizon cooperative difference game.- References.

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Book SynopsisThis book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.Trade Review“Each chapter ends with an exercise section … . While primarily addressed to researchers, the book can be used for graduate courses in optimization, by undergraduate and graduate students for theses and projects as well as by researchers and practitioners from other fields where tools from convex analysis, variational analysis and optimization play a role. All in one, the reviewer warmly recommends this book to anyone interested.” (Sorin-Mihai Grad, zbMATH 1506.90001, 2023)“This outstanding book will certainly be useful to anyone interested to learn convex analysis, in particular to graduate students and researchers in the field. Most parts of it can also serve as the basis of advanced courses on a variety of topics. In view of the excellence of this first volume, one can expect the best of the announced second one, which will deal with applications of convex analysis.” (Juan Enrique Martínez-Legaz, Mathematical Reviews, February, 2023)“Every chapter of the book has one section of exercises and one section of commentaries. These sections provide the reader with a lot of information and give him/her great benefits in self-learning. … The book under review has many things to offer and, surely, it will play an important role in the development of convex analysis … . The book is very useful for theoretical research and practical use. Thanks to the art of writing of the authors … .” (Nguyen Dong Yen, Journal of Global Optimization, Vol. 85, 2023)Table of ContentsFundamentals.- Basic theory of convexity.- Convex generalized differentiation.- Enhanced calculus and fenchel duality.- Variational techniques and further subgradient study.- Miscellaneous topics on convexity.- Convexified Lipschitzian analysis.- List of Figures.- Glossary of Notation and Acronyms.- Subject Index.

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Book SynopsisFollowing the successful PCS Auction conducted by the US Federal Communications Commission in 1994, auctions have replaced traditional ways of allocating valuable radio spectrum, a key resource for any mobile telecommunications operator. Spectrum auctions have raised billions of dollars worldwide and have become a role model for market-based approaches in the public and private sectors. The design of spectrum auctions is a central application of game theory and auction theory due to its importance in industry and the theoretical challenges it presents. Several auction formats have been developed with different properties addressing fundamental questions about efficiently selling multiple objects to a group of buyers. This comprehensive handbook features classic papers and new contributions by international experts on all aspects of spectrum auction design, including pros and cons of different auctions and lessons learned from theory, experiments, and the field, providing a valuable resTrade Review'This superb Handbook is a milestone in the progress of market design. It's a comprehensive analysis of designs, implementation, experimental testing, and bidding experience in auctions and similar markets for spectrum licenses. The authors achieved remarkable success in many auctions after the initial FCC auction began worldwide efforts to allocate licenses more efficiently via market mechanisms. The distinguished contributors report their solutions to difficult problems, the resulting performance, and remaining challenges.' Robert Wilson, Adams Distinguished Professor of Management, Stanford University'The papers in this volume highlight both the theoretical and the practical issues that arise in spectrum auctions. The book includes contributions from many of the world's leading economists, game theorists, optimizers, and computer scientists. Anyone interested in the practical application of market design and resource allocation will find this text an important reference.' Karla Hoffman, George Mason University, Virginia'Bichler and Goeree, both important contributors to the field, have curated an exceptional Handbook, which will be an invaluable resource for researchers and practitioners working on the design of auctions and secondary exchanges for spectrum and other applications with complex interdependencies.' Peter Bossaerts, Redmond Barry Distinguished Professor, University of Melbourne'Spectrum auctions are a remarkable example of 'technology transfer' from research to practice, with beautiful theoretical ideas informing current auction designs that regularly generate tens of billions of dollars in revenue. Bichler and Goeree have masterfully assembled the 'greatest hits' of this literature, ranging from the early papers that laid the foundations to the latest developments on the 2016 FCC Incentive Auction.' Tim Roughgarden, Stanford University'This Handbook is the answer to my search for a truly wholistic view on auction designs and will be an extremely valuable resource for consultations with regulatory authorities as well as bid strategy preparations.' Matthias Leonhard, DT Spectrum Projects, Deutsche TelekomTable of ContentsPreface; Part I. The Simultaneous Ascending Auction: 1. Putting auction theory to work: the simultaneous ascending auction; 2. An equilibrium analysis of the simultaneous ascending auction; 3. The efficiency of the FCC spectrum auctions; 4. Measuring the efficiency of an FCC spectrum auction; Part II. The Combinatorial Clock Auction Formats: 5. Combinatorial auction design; 6. The clock-proxy auction: a practical combinatorial auction design; 7. Spectrum auction design; 8. A practical guide to the combinatorial clock auction; 9. Market design and the evolution of the combinatorial clock auction; 10. Quadratic core-selecting payment rules for combinatorial auctions; 11. Core-selecting package auctions; 12. A new payment rule for core-selecting package auctions; 13. On the impossibility of core-selecting auctions; 14. Ascending combinatorial auctions with risk averse bidders; 15. Properties of the combinatorial clock auction; 16. Budget constraints combinatorial clock auctions; 17. (Un)expected bidder behavior in spectrum auctions: about inconsistent bidding and its impact on efficiency in the combinatorial clock auction; Part III. Alternative Auction Designs: 18. A combinatorial auction mechanism for airport time slot allocation; 19. A new and improved design for multiobject iterative auctions; 20. Hierarchical package bidding: a paper and pencil combinatorial auction; 21. Assignment messages and exchanges; 22. The product-mix auction: a new auction design for differentiated goods; 23. The continuous combinatorial auction architecture; 24. Coalition-based pricing in ascending combinatorial auctions; Part IV. Experimental Comparisons of Auction Designs: 25. Experiments testing multiobject allocation mechanisms; 26. Laboratory experimental testbeds: application to the PCS auction; 27. An experimental test of flexible combinatorial spectrum auction formats; 28. On the impact of package selection in combinatorial auctions: an experimental study in the context of spectrum auction design; 29. Do core-selecting combinatorial clock auctions always lead to high efficiency? An experimental analysis of spectrum auction designs; 30. Spectrum auction design: simple auctions for complex sales; Part V. The Bidders' Perspective: 31. Winning play in spectrum auctions; 32. Up in the air: GTE's experience in the MTA auction for personal communication services licenses; 33. Bidding complexities in the combinatorial clock auction; 34. Strategic bidding in combinatorial clock auctions – a bidder perspective; 35. Impact of budget-contraints on the efficiency of multi-lot spectrum auctions; Part VI. Secondary Markets and Exchanges: 36. Spectrum markets: motivation, challenges, and implications; 37. Designing the US incentive auction; 38. Solving the station repacking problem; 39. ICE: an expressive iterative combinatorial exchange; 40. ACE: a combinatorial market mechanism; Outlook.

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Book SynopsisGain an in-depth understanding of converter-interfaced energy storage systems with this unique text, covering modelling, dynamic behaviour, control, and stability analysis. Providing comprehensive coverage, it demonstrates the technical and economic aspects of energy storage systems, and provides a thorough overview of energy storage technologies. Several different modelling techniques are presented, including power system models, voltage-sourced converter models, and energy storage system models. Using a novel stochastic control approach developed by the authors, you will learn about the impact of energy storage on the dynamic interaction of microgrids with distribution and transmission systems. Compare the numerous real-world simulation data and numerical examples provided with your own models and control strategies. Accompanied online by a wealth of numerical examples and supporting data, this is the ideal text for graduate students, researchers, and industry professionals working iTrade Review'This is a timely and impressive book on an emerging and important topic. The comprehensive and in-depth overview of energy storage technologies, modelling, and dynamic simulation will make the book a valuable reference for practicing engineers and researchers working with the planning and operation of the future electric power system. The extensive list of references will be of great help for deepened studies.' Göran Andersson, Eidgenössische Technische Hochschule Zürich'Energy storage systems (ESS) are considered by many as the Holy Grail of the upcoming decarbonised future. From rooftop PV microsystems to giant pumped storage units, virtually all ESS are expected to be interfaced through power converters, for the sake of added flexibility and efficiency. This volume, co-authored by one of the most recognized experts in modelling, analysis and control of power systems dynamic phenomena, constitutes a self-contained and unique blend of general concepts, motivating factors and technical details, satisfying in this way the interests of a wide audience and filling an important gap in the technical literature.' Antonio Gomez-Exposito, Universidad de Sevilla'Excellent and timely material written by experienced authors! You must read this book.' Jean Mahseredjian, Polytechnique MontréalTable of ContentsPart I. Context: 1. Need for energy storage; 2. Technical and economic aspects; 3. Energy storage technologies; Part II. Modelling: 4. Power system model; 5. Voltage-sourced converter model; 6. Energy storage system models; Part III. Dynamic Analysis: 7. Comparison of dynamic models; 8. Control techniques; 9. Stability analysis; Part IV. Appendices.

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Book SynopsisA unique text integrating numerics, mathematics and applications to provide a hands-on approach to using optimization techniques, this mathematically accessible textbook emphasises conceptual understanding and importance of theorems rather than elaborate proofs. It allows students to develop fundamental optimization methods before delving into MATLAB''s optimization toolbox, and to link MATLAB''s results with the results from their own code. Following a practical approach, the text demonstrates several applications, from error-free analytic examples to truss (size) optimization, and 2D and 3D shape optimization, where numerical errors are inevitable. The principle of minimum potential energy is discussed to highlight the deep relationship between engineering and optimization. MATLAB code in every chapter illustrates key concepts and the text demonstrates the coupling between MATLAB and SOLIDWORKS for design optimization. A wide variety of optimization problems are covered including conTrade Review'Design Optimization using MATLAB and SOLIDWORKS by Dr. Suresh provides an excellent review of various optimization methods, especially for structural problems. Its introduction to MATLAB would help students who have had little experience with this software to become familiar with it quickly and apply it to some of the basic optimization problems.' Hamid Torab, Gannon University'Dr. Suresh's text brings his contributions to shape optimization into the classroom by connecting optimization, MATLAB, SOLIDWORKS, and SOLIDLAB into a single textbook. This text enables the reader to build upon this research accomplishment. I look forward to seeing what my students can achieve with this textbook at their fingertips.' Cameron Turner, Clemson UniversityTable of ContentsPreface; Table of Contents; 1. Introduction; 2. Modeling; 3. Introduction to MATLAB; 4. Unconstrained Optimization: Theory; 5. Unconstrained Optimization: Algorithms; 6. MATLAB Optimization Toolbox; 7. Constrained Optimization; 8. Special Classes of Problems; 9. Truss Analysis; 10. Size Optimization of Trusses; 11. Gradient Computation; 12. Finite Element Analysis in 2D; 13. Shape Optimization in 2D; 14. Finite Element Analysis in 3D; 15. SOLIDLAB: A SOLIDWORKS-MATLAB Interface; 16. Shape Optimization using SOLIDLAB; 17. Appendix; 18. References.

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Book SynopsisThis rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin''s Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering.Trade Review'High standards of linear control were established in the 1960s in pioneering works by R. Bellman, R. Kalman, and L. Pontryagin. However, this field of research remains active and is permanently enriched with new results and new applications, as the book by S. P. Bhattacharyya and L. H. Keel vividly demonstrates.' Boris Polyak, IFAC Fellow, Institute for Control Science, Moscow'One of the most valuable features of this book is that it integrates the pillars of control theory with recent advancements, resulting in an up-to-date treatment of the topic.' Antonio Visioli, University of BresciaTable of ContentsPreface; 1. A measurement-based approach to linear systems; 2. Classical control theory: a brief overview; 3. The [A,B,C,D] state variable model; 4. Modal structure of state space systems; 5. Controllability, observability and realization theory; 6. State feedback, observers and regulators; 7. The optimal linear quadratic regulator; 8. H¥ and H2 optimal control; 9. The linear multivariable servomechanism; 10. Robustness and fragility of control systems; 11. Analytical design of PID controllers; 12. Multivariable control using single input single output methods; Appendix; References; Index.

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Book SynopsisThis monograph presents smooth, unified, and generalized fractional programming problems, particularly advanced duality models for discrete min-max fractional programming. In the current, interdisciplinary, computer-oriented research environment, these programs are among the most rapidly expanding research areas in terms of their multi-faceted applications including problems ranging from robotics to money market portfolio management. The other more significant aspect of this monograph is in its consideration of minimax fractional integral type problems using higher order sonvexity and sounivexity notions. This is significant for the development of different types of duality models in terms of weak, strong, and strictly converse duality theorems, which can be handled by transforming them into generalized fractional programming problems. Fractional integral type programming is one of the fastest expanding areas of optimization, which feature several types of real-world problems. It can be applied to different branches of engineering (including multi-time multi-objective mechanical engineering problems) as well as to economics, to minimize a ratio of functions between given periods of time. Furthermore, it can be utilized as a resource in order to measure the efficiency or productivity of a system. In these types of problems, the objective function is given as a ratio of functions. For example, we consider a problem that deals with minimizing a maximum of several time-dependent ratios involving integral expressions.Table of ContentsFor more information, please visit our website at:https://novapublishers.com/shop/new-trends-in-fractional-programming/

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Book SynopsisOptimisation is the process of obtaining the most appropriate solution by providing certain constraints for the given purpose or purposes. Mathematically, optimisation can be briefly defined as minimising or maximising a function. In short, optimisation is to look for the best. The best found is called "optimum. Optimisation is used to accelerate decision-making processes and to solve real-life problems in an effective, accurate and real-time manner. In addition to the economic benefits, optimisation is also used as an effective method to include the preferences and constraints of customers, employers and employees in the decision process and to improve the quality of the resources in the system. The purpose of optimisation is to achieve the best result, the best goal. Improvements can be made to the current situation or situations to achieve the best result. One of the major shortcomings in optimisation and robotic is the transformation of theoretical knowledge into practice. The purpose of the book is to introduce students, teachers, researchers, and practitioners to new advances in this area. The book content includes theoretical and practical studies prepared with the academic contributions of scientists working in different fields. It was decided to publish each chapter in the book after being examined by the scientific board. As an editor, my duty is to ensure breadth, while the chapter authors treat the delegated chapters with depth. The book is designed for practitioners or researchers of all levels of expertise from novice to expert. Each of the book's individual topics could be considered as a compact, self-contained mini-book right under its title. The approach is to provide a framework and a set of techniques for evaluating and improving optimisation and robotic. It presents a specific set of solutions, mostly obtained from real world projects and experimental studies, for routine applications. It further highlights promising emerging techniques for research and exploration opportunities. The development team of this book wants to thank their colleagues who made contributions to this book by providing continuous encouragements and thorough reviews of the chapters of the book.Table of ContentsPreface; A Source Seeking Algorithm with Application to a Quadcopter Model; Activation Functions for Deep Learning in Smart Manufacturing; A New Approach to Kaiser and Gaussian Window Based Cosine Modulated Filter Bank Design; A Preliminary Study of Region Of Interest Based Functional Connectivity Analysis for Classification of MDD and Healthy Subjects Using Graph Metrics; Investigation of the Effect of Graphene Oxide and Aluminum Oxide Particles on the Mechanical Properties of Glass / Kevlar /Carbon Fiber Reinforced Epoxy Composites; Conversion from Conventional Power Distribution Networks to Smart Power Distribution Networks; A Parametric Study for Artificial Bee Colony Algorithm Used in Vehicle Routing Problem with Simultaneous Delivery and Pickup; Lightweighting Airborne Vehicles Structural Analysis of Carbon Fiber-Reinforced Aluminum and High Altitude Long Endurance New Drone: Octocopter Robot Unmanned Aerial Vehicles (UAVs) Design by Computational Fluid Dynamics and Finite Element Method; Index.

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Book SynopsisEconomics is a science which studies human behaviours as a relationship between ends and scarce means which have alternative uses. Since economic resources are scarce, optimisation forms an integral part in the study of economics. In addition, in the presence of imperfect market structure, externalities, imperfect information or public goods, the market fails to provide an efficient allocation mechanism. Optimisation of economic activities provides an effective remedial measure for market failures. This contributed volume collects advances in the studies of economics and optimisation. Contributions cover areas on analysis of optimal allocation of economic resources, economic optimisation techniques, the interface economics and optimisation, optimisation under market mechanism and history of development of optimisation techniques. The studies assembled in this volume are dedicated to the memory of a pioneering researcher and Nobel Laureate in the field of economic optimisation -- Leonid Vitalyevich Kantorovich. In his 100th birthday tribute in 2012, the International Conference Mathematics, Economic, Management: Kantorovich-100 in St-Petersburg was held in his memory. Selected papers from the conference are included in this Volume. In addition, contributed papers from authors who had worked closely with Kantorovich are also contained.

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