Quadratic Programming with Computer Programs
Published on 12. July 2017
400 pages
978-1-4987-3577-3 (ISBN)
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.
Reviews / Votes
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
More details
Series
Language
English
Place of publication
Philadelphia, PA
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Professional and scholarly
Illustrations
25 Illustrations, black and white
File size
2,80 MB
ISBN-13
978-1-4987-3577-3 (9781498735773)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Michael J. Best
Quadratic Programming with Computer Programs
Book
01/2023
1st Edition
Chapman & Hall/CRC
€78.17
Shipment within 10-20 days
Michael J. Best
Quadratic Programming with Computer Programs
Book
01/2017
1st Edition
Chapman & Hall/CRC
€133.69
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Person
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.
Content
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
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
