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1st Edition

Quadratic Programming with Computer Programs




ISBN 9781498735759
Published January 18, 2017 by Chapman and Hall/CRC
386 Pages - 25 B/W Illustrations

 
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Book Description

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.

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

 

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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

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