Description
Book SynopsisQuadratic programming is a mathematical technique that allows for the optimization of a quadratic function in several variables. QP is a subset of Operations Research and is the next higher lever of sophistication than Linear Programming. It is a key mathematical tool in Portfolio Optimization and structural plasticity. This is useful in Civil Engineering as well as Statistics.
Trade ReviewThis book is devoted to quadratic programming (QP) and parametric quadratic programming (PQP). It is a textbook which may be useful for students and many scientific researchers as well. It is richly illustrated with many examples and gures.The book starts with the presentation of some geometric facts on unconstrained QP problems, followed by the introduction of some QP models arising in portfolio optimization. The latter reflects the author's experience with such types of applications.The rest of the book is organized logically as is usually done in QP: unconstrained convex QP problems, QP with linear equality constraints, QP with linear inequality constraints, duality in quadratic programming, dual QP algorithms, general QP and PQP algorithms, the simplex method for QP and PQP and nonconvex QP.
Andrzej Stachurski~Mathematical Reviews, 2017
Table of ContentsGeometrical Examples
Geometry of a QP: Examples
Geometrical Examples
Optimality Conditions
Geometry of Quadratic Functions
Nonconvex QP’s
Portfolio Opimization
The Efficient Frontier
The Capital Market Line
QP Subject to Linear Equality Constraints
QP Preliminaries
QP Unconstrained: Theory
QP Unconstrained: Algorithm 1
QP with Linear Equality Constraints: Theory
QP with Linear Equality Constraints: Alg. 2
Quadratic Programming
QP Optimality Conditions
QP Duality
Unique and Alternate Optimal Solutions
Sensitivity Analysis
QP Solution Algorithms
A Basic QP Algorithm: Algorithm 3
Determination of an Initial Feasible Point
An Efficient QP Algorithm: Algorithm 4
Degeneracy and Its Resolution
A Dual QP Algorithm
Algorithm 5
General QP and Parametric QP Algorithms
A General QP Algorithm: Algorithm 6
A General Parametric QP Algorithm: Algorithm 7
Symmetric Matrix Updates
Simplex Method for QP and PQP
Simplex Method for QP: Algorithm 8
Simplex Method for Parametric QP: Algorithm 9
Nonconvex Quadratic Programming
Optimality Conditions
Finding a Strong Local Minimum: Algorithm 10
