Optimization Books
Springer Nonconvex Optimization in Mechanics
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£170.99
Springer Exercises in Graph Theory 19 Texts in the Mathematical Sciences
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£189.99
Springer Connectedness and Necessary Conditions for an Extremum Mathematics and Its Applications 431
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£85.49
Springer Minimax Theory and Applications 26 Nonconvex Optimization and Its Applications
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£85.49
Springer Estimators for Uncertain Dynamic Systems Mathematics and Its Applications 458
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£123.49
Springer Nonlinear Analysis Differential Equations and Control Proceedings of the NATO Advanced Ssudy Institute Universite De Montreal Canada July 27August 7 528 Nato Science Series C
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£85.49
Springer Nonlinear Analysis Differential Equations and Control Proceedings of the NATO Advanced Study Institute Universite De Montreal Canada July 27August 7 528 Nato Science Series C
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£85.49
Springer Functional Differential Equations Application of ismooth calculus 479 Mathematics and Its Applications
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£85.49
Springer The Theory of Anisotropic Elastic Plates 476 Mathematics and Its Applications
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£85.49
Springer Modern Optimisation Techniques in Power Systems
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£123.49
Springer Geometrical Methods in Variational Problems 485 Mathematics and Its Applications
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£85.49
Springer Semirings and their Applications
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£104.49
Springer Noniterative Coordination in Multilevel Systems 34 Nonconvex Optimization and Its Applications
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£89.99
Springer A Set of Examples of Global and Discrete Optimization
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£123.49
Springer Graph Theory for Programmers Algorithms for Processing Trees 515 Mathematics and Its Applications
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£85.49
Springer Optimality Conditions Abnormal and Degenerate Problems 526 Mathematics and Its Applications
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£44.99
Springer Geometry of PseudoFinsler Submanifolds 527 Mathematics and Its Applications
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£44.99
Springer Differential Geometry of Spray and Finsler Spaces
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£85.49
Springer Separable Programming Theory and Methods Applied Optimization 53
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£85.49
Springer Multiple Criteria Decision Analysis
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£208.99
Springer Fuzzy Modeling for Control 12 International Series in Intelligent Technologies
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£170.99
Springer Large Scale Linear and Integer Optimization A Unified Approach
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£427.49
Birkhauser Boston Semiconcave Functions HamiltonJacobi Equations and Optimal Control
Book SynopsisA comprehensive exposition of the properties of semiconcave functions and their various applications, particularly to optimal control problems. It is suitable for graduate students and researchers in optimal control, the calculus of variations, and PDEs.Trade Review"The main purpose of this book is to provide a systematic study of the notion of semiconcave functions, as well as a presentation of mathematical fields in which this notion plays a fundamental role. Many results are extracted from articles by the authors and their collaborators, with simplified—and often new—presentation and proofs.... One of the most attractive features of this book is the interplay between several fields of mathematical analysis.... Despite the many topics addressed in the book, the required mathematical background for reading it is limited because all the necessary notions are not only recalled, but also carefully explained, and the main results proved. The book will be found very useful by experts in nonsmooth analysis, nonlinear control theory and PDEs, in particular, as well as by advanced graduate students in this field. They will appreciate the many detailed examples, the clear proofs and the elegant style of presentation, the fairly comprehensive and up-to-date bibliography and the very pertinent historical and bibliographical comments at the end of each chapter." —Mathematical ReviewsTable of ContentsA Model Problem.- Semiconcave Functions.- Generalized Gradients and Semiconcavity.- Singularities of Semiconcave Functions.- Hamilton-Jacobi Equations.- Calculus of Variations.- Optimal Control Problems.- Control Problems with Exit Time.
£66.49
Birkhauser Boston Optimal Control and Viscosity Solutions of HamiltonJacobiBellman Equations Modern Birkhuser Classics
Book SynopsisOutline of the main ideas on a model problem.- Continuous viscosity solutions of Hamilton-Jacobi equations.- Optimal control problems with continuous value functions: unrestricted state space.- Optimal control problems with continuous value functions: restricted state space.- Discontinuous viscosity solutions and applications.- Approximation and perturbation problems.- Asymptotic problems.- Differential Games.Trade Review"The exposition is self-contained, clearly written and mathematically precise. The exercises and open problems…will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area. The book may be used by graduate students and researchers in control theory both as an introductory textbook, and as an up-to-date reference book." —Mathematical Reviews "The work is self-contained and is written in an accessible style with discussions of difficult questions on simplified model problems, with useful sections of bibliographical and historical notes and rich sets of proposed exercises at the end of each section. It may be easily used for graduate courses on various topics in control theory. We recommend it to both students and researchers interested in this area of applied mathematics." —Revue Roumaine de Mathématiques Pures et Appliquées "The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field. However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my oppinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." —Zentralblatt MATH "The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)... In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." —Acta Applicandae Mathematicae "The book originated from the lecture notes of courses taught by the authors, which is reflected in the style of presentation. Each chapter is enriched with a section of bibliographical and historical notes. The book can be recommended to specialists in PDEs, control theory, differential games, and related topics." —Mathematica Bohemica "As an outgrowth of lecture notes, this monograph purports to introduce and pursue the concept of viscosity solutions of the Hamilton-Jacobo-Bellman equations. It does so requiring but a relative modicum of mathematical knowledge... The book is written in a largely self-contained manner. In addition to bibliographical notes, exercises are provided as well." —Monatshefte für Mathematik "With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercises exciting to self control and active collaboration. Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." —ZAATable of ContentsPreface.- Basic notations.- Outline of the main ideas on a model problem.- Continuous viscosity solutions of Hamilton-Jacobi equations.- Optimal control problems with continuous value functions: unrestricted state space.- Optimal control problems with continuous value functions: restricted state space.- Discontinuous viscosity solutions and applications.- Approximation and perturbation problems.- Asymptotic problems.- Differential Games.- Numerical solution of Dynamic Programming.- Nonlinear H-infinity control by Pierpaolo Soravia.- Bibliography.- Index
£113.99
Taylor & Francis Ltd Optimization in Medicine and Biology 03
Book SynopsisThanks to recent advancements, optimization is now recognized as a crucial component in research and decision-making across a number of fields. Through optimization, scientists have made tremendous advances in cancer treatment planning, disease control, and drug development, as well as in sequencing DNA, and identifying protein structures. Optimization in Medicine and Biology provides researchers with a comprehensive, single-source reference that will enable them to apply the very latest optimization techniques to their work. With contributions from pioneering international experts this volume integrates strong foundational theory, good modeling techniques, and efficient and robust algorithms with relevant applications Divided into two sections, the first begins with mathematical programming techniques for medical decision making processes and demonstrates their application to optimizing pediatric vaccine formularies, kidney paired donation, and the cost-effectiveness Table of ContentsMedicine. Classification and Disease Prediction via Mathematical Programming. Using Influence Diagrams in Cost Effectiveness Analysis for Medical Decisions. Non-Bayesian Classification to Obtain High Quality Clinical Decisions. Optimizing Pediatric Vaccine Formularies. . Optimization Over Graphs for Kidney Paired Donation. Introduction to Radiation Therapy Planning Optimization. Beam Orientation Optimization Methods in Intensity Modulated Radiation Therapy Treatment Planning. Multileaf collimator shape matrix decomposition. Optimal Planning for Radiation Therapy. Biology. An Introduction to Systems Biology for Mathematical Programmers. Algorithms for Genomics Analysis. Computational Methods for Probe Design and Selection. An Implementation of Logical Analysis of Data for Oligo Probe Selection. A New Dihedral Angle Measure for Protein Secondary Prediction. Optimization of Tumor Virotherapy with Recombinant Measles Viruses. Combating Microbial Resistance to Antimicrobial Agents through Dosing Regimen Optimization. Appendix.
£237.34
Creative Media Partners, LLC Optimizing Mean Mission Duration for MultiplePayload Satellites
£22.75
Creative Media Partners, LLC Optimizing Mean Mission Duration for MultiplePayload Satellites
£14.96
Creative Media Partners, LLC A Decomposition Approach for the MultiModal ResourceConstrained MultiProject Scheduling Problem With Generalized Precedence and Expediting Resources
£17.95
Creative Media Partners, LLC Traveling Salesman Problem for Surveillance Mission Using Particle Swarm Optimization
£22.75
Creative Media Partners, LLC Traveling Salesman Problem for Surveillance Mission Using Particle Swarm Optimization
£14.09
Cambridge University Press Optimization for Chemical and Biochemical
Book SynopsisDiscover the subject of optimization in a new light with this modern and unique treatment. Includes a thorough exposition of applications and algorithms in sufficient detail for practical use, while providing you with all the necessary background in a self-contained manner. Features a deeper consideration of optimal control, global optimization, optimization under uncertainty, multiobjective optimization, mixed-integer programming and model predictive control. Presents a complete coverage of formulations and instances in modelling where optimization can be applied for quantitative decision-making. As a thorough grounding to the subject, covering everything from basic to advanced concepts and addressing real-life problems faced by modern industry, this is a perfect tool for advanced undergraduate and graduate courses in chemical and biochemical engineering.Trade Review'This book offers a very clear, uncluttered presentation of key ideas of optimisation in rigorous form and with plenty of examples from a decade of research and educational experience. It offers an exceptional resource for educators and students of optimisation methods, as well as a valuable reference text to practitioners.' Alexei Lapkin, University of Cambridge'This excellent book brings together important and up-to-date elements of the theory and practice of optimisation with application to chemical and biochemical engineering. It's an ideal reference for students on advanced courses or for researchers in the field.' Nilay Shah, Imperial CollegeTable of ContentsPart I. Overview of Optimization: 1. Introduction to optimization; Part II. From General Mathematical Background to General Nonlinear Programming Problems (NLP): 2. General concepts; 3. Convexity; 4. Quadratic functions; 5. Minimization in one dimension; 6. Unconstrained multivariate gradient-based minimization; 7. Constrained nonlinear programming problems (NLP); 8. Penalty and barrier function methods; 9. Interior point methods (IPMs), a detailed analysis; Part III. Formulation and Solution of Linear Programming (LP) Problem Models: 10. Introduction to LP models; 11. Numerical solution of LP problems using the simplex method; 12. A sampler of LP problem formulations; 13. Regression revisited, using LP to fit linear models; 14. Network flow problems; 15, LP and sensitivity analysis, in brief; Part IV. Further Topics in Optimization: 16. Multiobjective optimilzation problem (MOP); 17. Stochastic optimization problem (SOP); 18. Mixed integer programming; 19. Global optimization; 20. Optical control problems (dynamic optimization); 21. System identification and model predictive control.
£73.99
Cambridge University Press DataDriven Science and Engineering
Book SynopsisData-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art.
£51.99
Cambridge University Press Dynamic Systems and Control Engineering
Book SynopsisUsing a step-by-step approach, this textbook provides a modern treatment of the fundamental concepts, analytical techniques, and software tools used to perform multi-domain modeling, system analysis and simulation, linear control system design and implementation, and advanced control engineering. Chapters follow a progressive structure, which builds from modeling fundamentals to analysis and advanced control while showing the interconnections between topics, and solved problems and examples are included throughout. Students can easily recall key topics and test understanding using Review Note and Concept Quiz boxes, and over 200 end-of-chapter homework exercises with accompanying Concept Keys are included. Focusing on practical understanding, students will gain hands-on experience of many modern MATLAB tools, including Simulink and physical modeling in Simscape. With a solutions manual, MATLAB code, and Simulink/Simscape files available online, this is ideal for senior undergraduates Trade Review'Lucid and easy to read. It methodically explains classic control theory, from modeling of multi-domain systems to digital control. The detailed examples and end-of-chapter problems make it an excellent choice as a textbook for students in different engineering and science disciplines. MATLAB® and Simulink® instructions are a big plus.' Pezhman Hassanpour, California State Polytechnic University'Dynamic Systems and Control Engineering by Jalili and Candelino is one of the most organized and easily understood basic texts in this area. They have taken what is a nebulous subject for many students and made it less daunting through their use of numerous examples across several disciplines. The text is laid out well, logical from the basic systems modeling, to their analyses, and their control. They have taken a progressive approach to build on previous knowledge as the topics become more advanced. Their straightforward mathematical models are reinforced through MATLAB® and Simulink®, with basic user guides for the software. This allows the student to learn about controls by doing controls.' Robert Rabb, Penn State University'I have enjoyed reading this book very much for several reasons. This is the most complete text on dynamic systems and automatic control, with a rich set of examples and deep analytic treatment, along with an application viewpoint. The authors have rich experience in research and teaching in dynamic systems and control engineering in several world-class universities worldwide.' Reza N. Jazar, Royal Melbourne Institute of Technology UniversityTable of ContentsPart I. Modeling of Multi-Domain Dynamic Systems: 1. Introduction to Dynamic Systems; 2. Modeling of Mechanical Systems; 3. Modeling of Electrical Systems; 4. Modeling of Multi-Domain Systems; Part II. Analysis of Multi-Domain Dynamic Systems: 5. Dynamic System Response; 6. System Response Characteristics; 7. System Transfer Function Analysis; Part III. Introduction to Feedback Systems: 8. Analysis of Feedback Control Systems; 9. Root Locus Techniques; 10. Frequency Domain Methods; 11. Implementation of Feedback Control Systems; Part IV. Analysis and Feedback Control of Modern Systems: 12. State-Space Representation and Analysis; 13. State-Space Control System Design; 14. Advanced Topics in Control Engineering.
£89.99
Springer Young Measures on Topological Spaces With Applications in Control Theory and Probability Theory Mathematics and Its Applications 571
Book SynopsisAims to provides applications to Visintin and Reshetnyak type theorems (Chapters 6 and 8), existence of solutions to differential inclusions (Chapter 7), dynamical programming (Chapter 8) and the Central Limit Theorem in locally convex spaces (Chapter 9).Trade ReviewFrom the reviews: "This book presents a wealth of results on Young measures on topological spaces in a very general framework. It is very likely that it will become the reference and starting point for any further developments in the field." (Georg K. Dolzmann, Mathematical Reviews, 2005k)Table of ContentsPreface. Generalities, Preliminary results. Young Measures, the four Stable Topologies: S, M, N, W. Convergence in Probability of Young Measures (with some applications to stable convergence). Compactness. Strong Tightness. Young Measures on Banach Spaces. Application. Applications in Control Theory. Semicontinuity of Integral Functionals using Young Measures. Stable Convergence in Limit Theorems of Probability Theory.
£44.99
Springer Variational Calculus and Optimal Control
Book Synopsis0 Review of Optimization in ?d.- Problems.- One Basic Theory.- 1 Standard Optimization Problems.- 2 Linear Spaces and Gâteaux Variations.- 3 Minimization of Convex Functions.- 4 The Lemmas of Lagrange and Du Bois-Reymond.- 5 Local Extrema in Normed Linear Spaces.- 6 The Euler-Lagrange Equations.- Two Advanced Topics.- 7 Piecewise C1 Extremal Functions.- 8 Variational Principles in Mechanics.- 9 Sufficient Conditions for a Minimum.- Three Optimal Control.- 10 Control Problems and Sufficiency Considerations.- 11 Necessary Conditions for Optimality.- A.1. The Intermediate and Mean Value Theorems.- A.2. The Fundamental Theorem of Calculus.- A.3. Partial Integrals: Leibniz' Formula.- A.4. An Open Mapping Theorem.- A.5. Families of Solutions to a System of Differential Equations.- A.6. The Rayleigh Ratio.- Historical References.- Answers to Selected Problems.Table of Contents0 Review of Optimization in ?d.- Problems.- One Basic Theory.- 1 Standard Optimization Problems.- 1.1. Geodesic Problems.- (a) Geodesics in ?d.- (b) Geodesics on a Sphere.- (c) Other Geodesic Problems.- 1.2. Time-of-Transit Problems.- (a) The Brachistochrone.- (b) Steering and Control Problems.- 1.3. Isoperimetric Problems.- 1.4. Surface Area Problems.- (a) Minimal Surface of Revolution.- (b) Minimal Area Problem.- (c) Plateau’s Problem.- 1.5. Summary: Plan of the Text.- Notation: Uses and Abuses.- Problems.- 2 Linear Spaces and Gâteaux Variations.- 2.1. Real Linear Spaces.- 2.2. Functions from Linear Spaces.- 2.3. Fundamentals of Optimization.- Constraints.- Rotating Fluid Column.- 2.4. The Gâteaux Variations.- Problems.- 3 Minimization of Convex Functions.- 3.1. Convex Functions.- 3.2. Convex Integral Functions.- Free End-Point Problems.- 3.3. [Strongly] Convex Functions.- 3.4. Applications.- (a) Geodesics on a Cylinder.- (b) A Brachistochrone.- (c) A Profile of Minimum Drag.- (d) An Economics Problem.- (e) Minimal Area Problem.- 3.5. Minimization with Convex Constraints.- The Hanging Cable.- Optimal Performance.- 3.6. Summary: Minimizing Procedures.- Problems.- 4 The Lemmas of Lagrange and Du Bois-Reymond.- Problems.- 5 Local Extrema in Normed Linear Spaces.- 5.1. Norms for Linear Spaces.- 5.2. Normed Linear Spaces: Convergence and Compactness.- 5.3. Continuity.- 5.4. (Local) Extremal Points.- 5.5. Necessary Conditions: Admissible Directions.- 5.6*. Affine Approximation: The Fréchet Derivative.- Tangency.- 5.7. Extrema with Constraints: Lagrangian Multipliers.- Problems.- 6 The Euler-Lagrange Equations.- 6.1. The First Equation: Stationary Functions.- 6.2. Special Cases of the First Equation.- (a) When f = f(z).- (b) When f = f(x,z).- (c) When f = f(y,z).- 6.3. The Second Equation.- 6.4. Variable End Point Problems: Natural Boundary Conditions.- Jakob Bernoulli’s Brachistochrone.- Transversal Conditions*.- 6.5. Integral Constraints: Lagrangian Multipliers.- 6.6. Integrals Involving Higher Derivatives.- Buckling of a Column under Compressive Load.- 6.7. Vector Valued Stationary Functions.- The Isoperimetric Problem.- Lagrangian Constraints*.- Geodesics on a Surface.- 6.8*. Invariance of Stationarity.- 6.9. Multidimensional Integrals.- Minimal Area Problem.- Natural Boundary Conditions.- Problems.- Two Advanced Topics.- 7 Piecewise C1 Extremal Functions.- 7.1. Piecewise C1 Functions.- (a) Smoothing.- (b) Norms for ?1.- 7.2. Integral Functions on ?1.- 7.3. Extremals in ?1 [a, b]: The Weierstrass-Erdmann Corner Conditions.- A Sturm-Liouville Problem.- 7.4. Minimization Through Convexity.- Internal Constraints.- 7.5. Piecewise C1 Vector-Valued Extremals.- Minimal Surface of Revolution.- Hilbert’s Differentiability Criterion*.- 7.6*. Conditions Necessary for a Local Minimum.- (a) The Weierstrass Condition.- (b) The Legendre Condition.- Bolza’s Problem.- Problems.- 8 Variational Principles in Mechanics.- 8.1. The Action Integral.- 8.2. Hamilton’s Principle: Generalized Coordinates.- Bernoulli’s Principle of Static Equilibrium.- 8.3. The Total Energy.- Spring-Mass-Pendulum System.- 8.4. The Canonical Equations.- 8.5. Integrals of Motion in Special Cases.- Jacobi’s Principle of Least Action.- Symmetry and Invariance.- 8.6. Parametric Equations of Motion.7*. The Hamilton-Jacobi Equation.- 8.8. Saddle Functions and Convexity; Complementary Inequalities.- The Cycloid Is the Brachistochrone.- Dido’s Problem.- 8.9. Continuous Media.- (a) Taut String.- The Nonuniform String.- (b) Stretched Membrane.- Static Equilibrium of (Nonplanar) Membrane.- Problems.- 9 Sufficient Conditions for a Minimum.- 9.1. The Weierstrass Method.- 9.2. [Strict] Convexity of f(x,Y, Z).- 9.3. Fields.- Exact Fields and the Hamilton-Jacobi Equation*.- 9.4. Hilbert’s Invariant Integral.- The Brachistochrone*.- Variable End-Point Problems.- 9.5. Minimization with Constraints.- The Wirtinger Inequality.- 9.6*. Central Fields.- Smooth Minimal Surface of Revolution.- 9.7. Construction of Central Fields with Given Trajectory: The Jacobi Condition.- 9.8. Sufficient Conditions for a Local Minimum.- (a) Pointwise Results.- Hamilton’s Principle.- (b) Trajectory Results.- 9.9*. Necessity of the Jacobi Condition.- 9.10. Concluding Remarks.- Problems.- Three Optimal Control.- 10 Control Problems and Sufficiency Considerations.- 10.1. Mathematical Formulation and Terminology.- 10.2. Sample Problems.- (a) Some Easy Problems.- (b) A Bolza Problem.- (c) Optimal Time of Transit.- (d) A Rocket Propulsion Problem.- (e) A Resource Allocation Problem.- (f) Excitation of an Oscillator.- (g) Time-Optimal Solution by Steepest Descent.- 10.3. Sufficient Conditions Through Convexity.- Linear State-Quadratic Performance Problem.- 10.4. Separate Convexity and the Minimum Principle.- Problems.- 11 Necessary Conditions for Optimality.- 11.1. Necessity of the Minimum Principle.- (a) Effects of Control Variations.- (b) Autonomous Fixed Interval Problems.- Oscillator Energy Problem.- (c) General Control Problems.- 11.2. Linear Time-Optimal Problems.- Problem Statement.- A Free Space Docking Problem.- 11.3. General Lagrangian Constraints.- (a) Control Sets Described by Lagrangian Inequalities.- (b)* Variational Problems with Lagrangian Constraints.- (c) Extensions.- Problems.- A.1. The Intermediate and Mean Value Theorems.- A.2. The Fundamental Theorem of Calculus.- A.3. Partial Integrals: Leibniz’ Formula.- A.4. An Open Mapping Theorem.- A.5. Families of Solutions to a System of Differential Equations.- A.6. The Rayleigh Ratio.- Historical References.- Answers to Selected Problems.
£49.99
Springer Functions of Several Variables
Book Synopsis1 Euclidean spaces.- 1.1 The real number system.- 1.2 Euclidean En.- 1.3 Elementary geometry of En.- 1.4 Basic topological notions in En.- *1.5 Convex sets.- 2 Elementary topology of En.- 2.1 Functions.- 2.2 Limits and continuity of transformations.- 2.3 Sequences in En.- 2.4 Bolzano-Weierstrass theorem.- 2.5 Relative neighborhoods, continuous transformations.- 2.6 Topological spaces.- 2.7 Connectedness.- 2.8 Compactness.- 2.9 Metric spaces.- 2.10 Spaces of continuous functions.- *2.11 Noneuclidean norms on En.- 3 Differentiation of real-valued functions.- 3.1 Directional and partial derivatives.- 3.2 Linear functions.- **3.3 Difierentiable functions.- 3.4 Functions of class C(q).- 3.5 Relative extrema.- *3.6 Convex and concave functions.- 4 Vector-valued functions of several variables.- 4.1 Linear transformations.- 4.2 Affine transformations.- 4.3 Differentiable transformations.- 4.4 Composition.- 4.5 The inverse function theorem.- 4.6 The implicit function theorem.- 4.7 Manifolds.- 4Table of Contents1 Euclidean spaces.- 1.1 The real number system.- 1.2 Euclidean En.- 1.3 Elementary geometry of En.- 1.4 Basic topological notions in En.- *1.5 Convex sets.- 2 Elementary topology of En.- 2.1 Functions.- 2.2 Limits and continuity of transformations.- 2.3 Sequences in En.- 2.4 Bolzano-Weierstrass theorem.- 2.5 Relative neighborhoods, continuous transformations.- 2.6 Topological spaces.- 2.7 Connectedness.- 2.8 Compactness.- 2.9 Metric spaces.- 2.10 Spaces of continuous functions.- *2.11 Noneuclidean norms on En.- 3 Differentiation of real-valued functions.- 3.1 Directional and partial derivatives.- 3.2 Linear functions.- **3.3 Difierentiable functions.- 3.4 Functions of class C(q).- 3.5 Relative extrema.- *3.6 Convex and concave functions.- 4 Vector-valued functions of several variables.- 4.1 Linear transformations.- 4.2 Affine transformations.- 4.3 Differentiable transformations.- 4.4 Composition.- 4.5 The inverse function theorem.- 4.6 The implicit function theorem.- 4.7 Manifolds.- 4.8 The multiplier rule.- 5 Integration.- 5.1 Intervals.- 5.2 Measure.- 5.3 Integrals over En.- 5.4 Integrals over bounded sets.- 5.5 Iterated integrals.- 5.6 Integrals of continuous functions.- 5.7 Change of measure under affine transformations.- 5.8 Transformation of integrals.- 5.9 Coordinate systems in En.- 5.10 Measurable sets and functions; further properties.- 5.11 Integrals: general definition, convergence theorems.- 5.12 Differentiation under the integral sign.- 5.13 Lp-spaces.- 6 Curves and line integrals.- 6.1 Derivatives.- 6.2 Curves in En.- 6.3 Differential 1-forms.- 6.4 Line integrals.- *6.5 Gradient method.- *6.6 Integrating factors; thermal systems.- 7 Exterior algebra and differential calculus.- 7.1 Covectors and differential forms of degree 2.- 7.2 Alternating multilinear functions.- 7.3 Multicovectors.- 7.4 Differential forms.- 7.5 Multivectors.- 7.6 Induced linear transformations.- 7.7 Transformation law for differential forms.- 7.8 The adjoint and codifferential.- *7.9 Special results for n = 3.- *7.10 Integrating factors (continued).- 8 Integration on manifolds.- 8.1 Regular transformations.- 8.2 Coordinate systems on manifolds.- 8.3 Measure and integration on manifolds.- 8.4 The divergence theorem.- *8.5 Fluid flow.- 8.6 Orientations.- 8.7 Integrals of r-forms.- 8.8 Stokes’s formula.- 8.9 Regular transformations on submanifolds.- 8.10 Closed and exact differential forms.- 8.11 Motion of a particle.- 8.12 Motion of several particles.- Axioms for a vector space.- Mean value theorem; Taylor’s theorem.- Review of Riemann integration.- Monotone functions.- References.- Answers to problems.
£53.99
Springer New York Linear and Nonlinear Optimization 253 International Series in Operations Research Management Science
Book SynopsisThis textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields.Trade Review“The historical notes in the book are interesting and well placed. … The book’s list of important references is quite complete. … this book is destined to become a classic in the field for beginning graduate students in optimization.” (S. Zlobec, Mathematical Reviews, January, 2018)Table of ContentsChapter 1. LP Models and Applications.- Chapter 2. Linear Equations and Inequalities.- Chapter 3. The Simplex Algorithm.- Chapter 4. The Simplex Algorithm Continued.- Chapter 5. Duality and the Dual Simplex Algorithm.- Chapter 6. Postoptimality Analysis.- Chapter 7. Some Computational Considerations.- Chapter 8. NLP Models and Applications.- Chapter 9. Unconstrained Optimization.- Chapter 10. Descent Methods.- Chapter 11. Optimality Conditions.- Chapter 12. Problems with Linear Constraints.- Chapter 13. Problems with Nonlinear Constraints.- Chapter 14. Interior-Point Methods.
£85.49
Springer Nature Switzerland AG Probabilistic Theory of Mean Field Games with
Book SynopsisThis two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions.Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.Trade Review“The text is very well-written and can be used to study the theory on various levels. It develops systematically from the wealth of motivating examples and heuristical considerations, through the carefully chosen collection of in-depth explained preliminaries, to the extensive nontrivial theory explained in full detail. … The book is highly recommended for those interested in the foundations and the up-to-date development of MFGs, as well as in the general area of stochastic control and related issues of analysis and probability.” (Vassili, Mathematical Reviews, January, 2019)Table of ContentsPreface to Volume I.- Part I: The Probabilistic Approach to Mean Field Games.- Learning by Examples: What is a Mean Field Game?.- Probabilistic Approach to Stochastic Differential Games.- Stochastic Differential Mean Field Games.- FBSDEs and the Solution of MFGs without Common Noise.- Part II: Analysis on Wasserstein Space and Mean Field Control.- Spaces of Measures and Related Differential Calculus.- Optimal Control of SDEs of McKean-Vlasov Type.- Epologue to Volume I.- Extensions for Volume I. References.- Indices.
£123.49
Springer Nature Switzerland AG First-order and Stochastic Optimization Methods for Machine Learning
Book SynopsisThis book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.Table of ContentsMachine Learning Models.- Convex Optimization Theory.- Deterministic Convex Optimization.- Stochastic Convex Optimization.- Convex Finite-sum and Distributed Optimization.- Nonconvex Optimization.- Projection-free Methods.- Operator Sliding and Decentralized Optimization.
£82.49
Springer Nature Switzerland AG Convex Analysis for Optimization: A Unified Approach
Book SynopsisThis textbook offers graduate students a concise introduction to the classic notions of convex optimization. Written in a highly accessible style and including numerous examples and illustrations, it presents everything readers need to know about convexity and convex optimization. The book introduces a systematic three-step method for doing everything, which can be summarized as "conify, work, deconify". It starts with the concept of convex sets, their primal description, constructions, topological properties and dual description, and then moves on to convex functions and the fundamental principles of convex optimization and their use in the complete analysis of convex optimization problems by means of a systematic four-step method. Lastly, it includes chapters on alternative formulations of optimality conditions and on illustrations of their use."The author deals with the delicate subjects in a precise yet light-minded spirit... For experts in the field, this book not only offers a unifying view, but also opens a door to new discoveries in convexity and optimization...perfectly suited for classroom teaching." Shuzhong Zhang, Professor of Industrial and Systems Engineering, University of MinnesotaTrade Review“The book is a valuable contribution to the topic of convex analysis. … A seasoned researcher in convex analysis and optimization will find this book more of a curiosity of possible interest. … Numerous examples and exercises are supplied at the end of each chapter. This book will provide a useful companion to other books on convex analysis and optimization when developing an introductory course in the area.” (Andrew C. Eberhard, Mathematical Reviews, August 2022)Table of ContentsConvex Sets: Basic properties.- Convex Sets: Binary Operations.- Convex Sets: Topological Properties.- Convex Sets: Dual Description.- Convex Functions: Basic Properties.- Convex Functions: Dual Description.- Convex Problems: The Main Questions.- Optimality Conditions: Reformulations.- Application to Convex Problems.
£66.49
Springer Nature Switzerland AG Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems
Book SynopsisThis book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.Table of Contents1.- Some Elements of Linear-Quadratic Optimal Controls.- 2. Linear-Quadratic Two-Person Differential Games.- 3. Mean-Field Linear-Quadratic Optimal Controls.
£41.24
Springer Nature Switzerland AG Advancing Parametric Optimization: On Multiparametric Linear Complementarity Problems with Parameters in General Locations
Book SynopsisThe theory presented in this work merges many concepts from mathematical optimization and real algebraic geometry. When unknown or uncertain data in an optimization problem is replaced with parameters, one obtains a multi-parametric optimization problem whose optimal solution comes in the form of a function of the parameters.The theory and methodology presented in this work allows one to solve both Linear Programs and convex Quadratic Programs containing parameters in any location within the problem data as well as multi-objective optimization problems with any number of convex quadratic or linear objectives and linear constraints. Applications of these classes of problems are extremely widespread, ranging from business and economics to chemical and environmental engineering. Prior to this work, no solution procedure existed for these general classes of problems except for the recently proposed algorithmsTable of Contents1. Introduction.- 2. Background on mpLCP.- 3. Algebraic Properties of Invariancy Regions.- 4. Phase 2: Partitioning the Parameter Space.- 5. Phase 1: Determining an Initial Feasible Solution.- 6. Further Considerations.- 7. Assessment of Performance.- 8. Conclusion.- Appendix A. Tableaux for Example 2.1.- Appendix B. Tableaux for Example 2.2.- References.
£41.24
Springer Nature Switzerland AG Riemannian Optimization and Its Applications
Book SynopsisThis brief describes the basics of Riemannian optimization—optimization on Riemannian manifolds—introduces algorithms for Riemannian optimization problems, discusses the theoretical properties of these algorithms, and suggests possible applications of Riemannian optimization to problems in other fields.To provide the reader with a smooth introduction to Riemannian optimization, brief reviews of mathematical optimization in Euclidean spaces and Riemannian geometry are included. Riemannian optimization is then introduced by merging these concepts. In particular, the Euclidean and Riemannian conjugate gradient methods are discussed in detail. A brief review of recent developments in Riemannian optimization is also provided. Riemannian optimization methods are applicable to many problems in various fields. This brief discusses some important applications including the eigenvalue and singular value decompositions in numerical linear algebra, optimal model reduction in control engineering, and canonical correlation analysis in statistics.Trade Review“The author successfully presents all of this varied material using a consistent and modern notation. … The book meticulously provides references with a comprehensive list at the end. It includes information about software libraries that implement Riemannian optimization in MATLAB, Python, R, C++, and Julia. Both the proofs and calculations in the examples are given with sufficient detail using a consistent notation.” (Anders Linnér, Mathematical Reviews, October, 2022)“The book is a very nice introductory reference for students, engineers, and practitioners to get started in the field of Riemannian optimization. … A highlight of the book is that it reviews the most important work in the field and also mentions current research topics. Thus, I also highly recommended it to researchers getting a broad overview of what is currently studied in the field, without being too detailed or theoretical.” (Lena Sembach, SIAM Review, Vol. 64 (2), June, 2022)Table of ContentsIntroduction.- Preliminaries and Overview of Euclidean Optimization.- Unconstrained Optimization on Riemannian Manifolds.- Conjugate Gradient Methods on Riemannian Manifolds.- Applications of Riemannian Optimization.- Recent Developments in Riemannian Optimization.
£54.99
Springer Nature Switzerland AG Bayesian Optimization with Application to Computer Experiments
Book SynopsisThis book introduces readers to Bayesian optimization, highlighting advances in the field and showcasing its successful applications to computer experiments. R code is available as online supplementary material for most included examples, so that readers can better comprehend and reproduce methods. Compact and accessible, the volume is broken down into four chapters. Chapter 1 introduces the reader to the topic of computer experiments; it includes a variety of examples across many industries. Chapter 2 focuses on the task of surrogate model building and contains a mix of several different surrogate models that are used in the computer modeling and machine learning communities. Chapter 3 introduces the core concepts of Bayesian optimization and discusses unconstrained optimization. Chapter 4 moves on to constrained optimization, and showcases some of the most novel methods found in the field. This will be a useful companion to researchers and practitioners working with computer experiments and computer modeling. Additionally, readers with a background in machine learning but minimal background in computer experiments will find this book an interesting case study of the applicability of Bayesian optimization outside the realm of machine learning. Table of Contents1. Computer experiments.- 2. Surrogate models.- 3. Unconstrained optimization.- 4. Constrained optimization.
£54.99
Springer Nature Switzerland AG Calculus of One Variable
Book SynopsisThis book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course. Table of ContentsSequence and Series of Real Numbers.- Limit, Continuity and Differentiability of Functions.- Definite Integral.- Improper Integrals.- Sequence and Series of Functions.- Fourier Series.- References.- Index.
£44.99
Springer Handbook of AI and Data Sciences for Sleep Disorders
Book SynopsisEmpowering Sleep Health: Unleashing the Potential of Artificial Intelligence and Data Science in Sleep Disorders.- Polysomnography Raw Data Extraction, Exploration, and Preprocessing.- Sleep stage probabilities derived from neurological or cardio-respiratory signals by means of artificial intelligence.- From Screening at Clinic to Diagnosis at Home: How AI/ ML/DL Algorithms are Transforming Sleep Apnea Detection.- Modeling and Analysis of Mechanical Work of Breathing.- A Probabilistic Perspective: Bayesian Neural Network for Sleep Apnea Detection.- Automatic and machine learning methods for detection and characterization of REM sleep behavior disorder.- Sleep Cyclic Alternating Pattern (CAP) as a Neurophysiological Marker of Brain Health.- Deep Learning with Electrocardiograms.- Machine learning automated analysis applied to mandibular jaw movements during sleep: a window on polysomnography.- Nightmare disorder: An Overview.
£119.99
Springer Dynamics of Disasters
£113.99
Springer Artificial Intelligence Optimization and Data Sciences in Sports
Book SynopsisChapter 1. Artificial Intelligence, Optimization, and Data Sciences in Sports: Editorial.- Chapter 2. Machine Learning for Soccer Match Result Prediction.- Chapter 3. Machine learning for prediction of the index of effec-tiveness in cycling.- Chapter 4. Machine Learning in Biomechanics: Key Applications and Limitations in Walking, Running, and Sports Movements.- Chapter 5. Artificial Intelligence & Machine Learning-Based Data Analytics for Sports. General Overview & NBA Case Study.- Chapter 6. An ecological dynamics approach to the use of Artificial Intelligence and Machine Learning to analyse performance in football.- Chapter 7. A Supervised Learning Approach for Evaluating Football Performances.- Chapter 8. Bridging Route based Cycling Training with Digital Twins.- Chapter 9. Perspectives of Artificial Intelligence in Training and Exercise.- Chapter 10. A fuzzy model for optimise the football rule assuring spectacle, fair play, objectivity and ethics.- Chapter 11. Physical Efficiency in Soccer: Relevance, Correlations and Impacts using AI Methods.- Chapter 12. A PageRank-Based Method for College Football Recruiting Rankings.- Chapter 13. APPLICATIONS OF IMPROVEMENTS TO THE PYTHAGOREAN WON-LOST EXPECTATION IN OPTIMIZING ROSTERS.
£123.49