Overview

This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequalities. One special feature of the book is that when a certain property of a characteristic map or function is investigated, the authors always try first to establish necessary conditions for it to hold, then they go on to study whether the obtained necessary conditions are also sufficient ones. This helps to clarify the structures of the two classes of problems under consideration. The qualitative results can be used for dealing with algorithms and applications related to quadratic programming problems and affine variational inequalities.

Full Product Details

Author:   Gue Myung Lee ,  N.N. Tam ,  Nguyen Dong Yen
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of hardcover 1st ed. 2005
Volume:   78
Dimensions:   Width: 15.50cm , Height: 1.80cm , Length: 23.50cm
Weight:   0.551kg
ISBN:  

9781441937131

ISBN 10:   1441937137
Pages:   346
Publication Date:   06 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Quadratic Programming Problems.- Existence Theorems for Quadratic Programs.- Necessary and Sufficient Optimality Conditions for Quadratic Programs.- Properties of the Solution Sets of Quadratic Programs.- Affine Variational Inequalities.- Solution Existence for Affine Variational Inequalities.- Upper-Lipschitz Continuity of the Solution Map in Affine Variational Inequalities.- Linear Fractional Vector Optimization Problems.- The Traffic Equilibrium Problem.- Upper Semicontinuity of the KKT Point Set Mapping.- Lower Semicontinuity of the KKT Point Set Mapping.- Continuity of the Solution Map in Quadratic Programming.- Continuity of the Optimal Value Function in Quadratic Programming.- Directional Differentiability of the Optimal Value Function.- Quadratic Programming under Linear Perturbations: I. Continuity of the Solution Maps.- Quadratic Programming under Linear Perturbations: II. Properties of the Optimal Value Function.- Quadratic Programming under Linear Perturbations: III. The Convex Case.- Continuity of the Solution Map in Affine Variational Inequalities.

Reviews

From the reviews: This book presents a detailed exposition of qualitative results for quadratic programming (QP) and affine variational inequalities (AVI). Both topics are developed into a unifying approach. (Walter Gomez Bofill, Zentralblatt MATH, Vol. 1092 (18), 2006) This book presents a theory of qualitative aspects of nonconvex quadratic programs and affine variational inequalities. ... Applications to fractional vector optimization problems and traffic equilibrium problems are discussed, too. The book is a valuable collection of many basic ideas and results for these classes of problems, and it may be recommended to researchers and advanced students not only in the field of optimization, but also in other fields of applied mathematics. (D. Klatte, Mathematical Reviews, Issue 2006 e) This book presents a qualitative study of nonconvex quadratic programs and affine variational inequalities. ... Most of the proofs are presented in a detailed and elementary way. ... Whenever possible, the authors give examples illustrating their results. ... In summary, this book can be recommended for advanced students in applied mathematics due to the clear and elementary style of presentation. ... this book can be serve as an interesting reference for researchers in the field of quadratic programming, finite dimensional variational inequalities and complementarity problems. (M. Stingl, Mathemataical Methods of Operations Research, Vol. 65, 2007)

From the reviews: This book presents a detailed exposition of qualitative results for quadratic programming (QP) and affine variational inequalities (AVI). Both topics are developed into a unifying approach. (Walter Gomez Bofill, Zentralblatt MATH, Vol. 1092 (18), 2006) This book presents a theory of qualitative aspects of nonconvex quadratic programs and affine variational inequalities. ... Applications to fractional vector optimization problems and traffic equilibrium problems are discussed, too. The book is a valuable collection of many basic ideas and results for these classes of problems, and it may be recommended to researchers and advanced students not only in the field of optimization, but also in other fields of applied mathematics. (D. Klatte, Mathematical Reviews, Issue 2006 e) This book presents a qualitative study of nonconvex quadratic programs and affine variational inequalities. ... Most of the proofs are presented in a detailed and elementary way. ... Whenever possible, the authors give examples illustrating their results. ... In summary, this book can be recommended for advanced students in applied mathematics due to the clear and elementary style of presentation. ... this book can be serve as an interesting reference for researchers in the field of quadratic programming, finite dimensional variational inequalities and complementarity problems. (M. Stingl, Mathemataical Methods of Operations Research, Vol. 65, 2007)

From the reviews: This book presents a detailed exposition of qualitative results for quadratic programming (QP) and affine variational inequalities (AVI). Both topics are developed into a unifying approach. (Walter Gomez Bofill, Zentralblatt MATH, Vol. 1092 (18), 2006) This book presents a theory of qualitative aspects of nonconvex quadratic programs and affine variational inequalities. ! Applications to fractional vector optimization problems and traffic equilibrium problems are discussed, too. The book is a valuable collection of many basic ideas and results for these classes of problems, and it may be recommended to researchers and advanced students not only in the field of optimization, but also in other fields of applied mathematics. (D. Klatte, Mathematical Reviews, Issue 2006 e) This book presents a qualitative study of nonconvex quadratic programs and affine variational inequalities. ! Most of the proofs are presented in a detailed and elementary way. ! Whenever possible, the authors give examples illustrating their results. ! In summary, this book can be recommended for advanced students in applied mathematics due to the clear and elementary style of presentation. ! this book can be serve as an interesting reference for researchers in the field of quadratic programming, finite dimensional variational inequalities and complementarity problems. (M. Stingl, Mathemataical Methods of Operations Research, Vol. 65, 2007)

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