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Set-valued Optimization

An Introduction with Applications

  • Akhtar A. Khan
  • Christiane Tammer
  • Constantin Zălinescu

Part of the Vector Optimization book series (VECTOROPT)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 1-10
  3. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 11-76
  4. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 77-108
  5. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 109-211
  6. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 213-248
  7. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 249-273
  8. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 275-306
  9. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 307-348
  10. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 349-368
  11. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 369-397
  12. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 399-508
  13. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 509-604
  14. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 605-643
  15. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 645-661
  16. Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 663-725
  17. Back Matter
    Pages 727-765

About this book

Introduction

Set-valued optimization is a vibrant and expanding branch of mathematics that deals with optimization problems where the objective map and/or the constraints maps are set-valued maps acting between certain spaces. Since set-valued maps subsumes single valued maps, set-valued optimization provides an important extension and unification of the scalar as well as the vector optimization problems. Therefore this relatively new discipline has justifiably attracted a great deal of attention in recent years. This book presents, in a unified framework, basic properties on ordering relations, solution concepts for set-valued optimization problems, a detailed description of convex set-valued maps, most recent developments in separation theorems, scalarization techniques, variational principles, tangent cones of first and higher order, sub-differential of set-valued maps, generalized derivatives of set-valued maps, sensitivity analysis, optimality conditions, duality, and applications in economics among other things.

Keywords

Hahn-Banach extension cone properties existence theorem minimal point nonconvex separation variational analysis

Authors and affiliations

  • Akhtar A. Khan
    • 1
  • Christiane Tammer
    • 2
  • Constantin Zălinescu
    • 3
  1. 1.Rochester Institute of Technology School of Mathematical SciencesRochesterUSA
  2. 2.HalleGermany
  3. 3.University "Al. I. Cuza" Iasi Faculty of MathematicsIasiRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-54265-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2015
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-54264-0
  • Online ISBN 978-3-642-54265-7
  • Series Print ISSN 1867-8971
  • Series Online ISSN 1867-898X
  • Buy this book on publisher's site
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