Skip to main content
SpringerLink
Log in

Quadratic Programming and Affine Variational Inequalities

A Qualitative Study

  • Book
  • © 2005

Overview

Authors:
  1. Gue Myung Lee

    1. Pukyong National University, Republic of Korea

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Nguyen Nang Tam

    1. Hanoi Pedagogical Institute No. 2, Vietnam

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Nguyen Dong Yen

    1. Vietnamese Academy of Science and Technology, Vietnam

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequalities

Part of the book series: Nonconvex Optimization and Its Applications (NOIA, volume 78)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (18 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Quadratic Programming Problems

    Pages 1-28

  3. Existence Theorems for Quadratic Programs

    Pages 29-44

  4. Necessary and Sufficient Optimality Conditions for Quadratic Programs

    Pages 45-63

  5. Properties of the Solution Sets of Quadratic Programs

    Pages 65-84

  6. Affine Variational Inequalities

    Pages 85-102

  7. Solution Existence for Affine Variational Inequalities

    Pages 103-118

  8. Upper-Lipschitz Continuity of the Solution Map in Affine Variational Inequalities

    Pages 119-142

  9. Linear Fractional Vector Optimization Problems

    Pages 143-154

  10. The Traffic Equilibrium Problem

    Pages 155-162

  11. Upper Semicontinuity of the KKT Point Set Mapping

    Pages 163-194

  12. Lower Semicontinuity of the KKT Point Set Mapping

    Pages 195-211

  13. Continuity of the Solution Map in Quadratic Programming

    Pages 213-222

  14. Continuity of the Optimal Value Function in Quadratic Programming

    Pages 223-238

  15. Directional Differentiability of the Optimal Value Function

    Pages 239-257

  16. Quadratic Programming under Linear Perturbations: I. Continuity of the Solution Maps

    Pages 259-268

  17. Quadratic Programming under Linear Perturbations: II. Properties of the Optimal Value Function

    Pages 269-290

  18. Quadratic Programming under Linear Perturbations: III. The Convex Case

    Pages 291-305

  19. Continuity of the Solution Map in Affine Variational Inequalities

    Pages 307-327

  20. Back Matter

    Pages 329-345
    Download chapter PDF
Back to top

Keywords

About this book

Quadratic programs and affine variational inequalities represent two fundamental, closely-related classes of problems in the t,heories of mathematical programming and variational inequalities, resp- tively. This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequ- ities. The first seven chapters introduce the reader step-by-step to the central issues concerning a quadratic program or an affine variational inequality, such as the solution existence, necessary and sufficient conditions for a point to belong to the solution set, and properties of the solution set. The subsequent two chapters discuss briefly two concrete nlodels (linear fractional vector optimization and the traffic equilibrium problem) whose analysis can benefit a lot from using the results on quadratic programs and affine variational inequalities. There are six chapters devoted to the study of conti- ity and/or differentiability properties of the characteristic maps and functions in quadratic programs and in affine variational inequa- ties where all the components of the problem data are subject to perturbation. Quadratic programs and affine variational inequa- ties under linear perturbations are studied in three other chapters. One special feature of the presentation is that when a certain pr- erty of a characteristic map or function is investigated, we always try first to establish necessary conditions for it to hold, then we go on to study whether the obtained necessary conditions are suf- cient ones. This helps to clarify the structures of the two classes of problems under consideration.

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 Gómez 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)

Authors and Affiliations

  • Pukyong National University, Republic of Korea

    Gue Myung Lee

  • Hanoi Pedagogical Institute No. 2, Vietnam

    Nguyen Nang Tam

  • Vietnamese Academy of Science and Technology, Vietnam

    Nguyen Dong Yen

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation