Overview

Quadratic 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.

Full Product Details

Author:   Michael J. Best
Publisher:   Taylor & Francis Ltd
Imprint:   CRC Press
Weight:   0.675kg
ISBN:  

9781032476940

ISBN 10:   103247694
Pages:   400
Publication Date:   21 January 2023
Audience:   College/higher education ,  General/trade ,  Tertiary & Higher Education ,  General
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Geometrical 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

Reviews

This 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

This 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

Author Information

Michael J. Best is Professor Emeritus in the Department of Combinatorics and Optimization at the University of Waterloo. He is only the second person to receive a B.Math degree from the University of Waterloo and holds a PhD from UC-Berkeley. Michael is also the author of Portfolio Optimzation, published by CRC Press.

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