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Quadratic Programming with Computer Programs de Michael J. Best

Quadratic Programming with Computer Programs: Advances in Applied Mathematics

Autor Michael J. Best
en Limba Engleză Paperback – 21 ian 2023
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.
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Specificații

ISBN-13: 9781032476940
ISBN-10: 103247694X
Pagini: 400
Ilustrații: 25
Dimensiuni: 178 x 254 mm
Greutate: 0.68 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Advances in Applied Mathematics

Cuprins

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


 

Recenzii

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

Notă biografică

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.

Descriere

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 E