Quadratic Programming with Computer Programs

by Michael J. Best

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.

Product Details

ISBN-13:	9781032476940
Publisher:	CRC Press
Publication date:	01/21/2023
Series:	Advances in Applied Mathematics
Pages:	400
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

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.

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

Editorial 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

From the Publisher