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  • © 2015

Set-valued Optimization

An Introduction with Applications

  • The first book on the growing subject of set-valued optimization
  • A highly simplified introduction to many complex issues in set-valued and vector optimization
  • Most up-to-date results which were so far only available in research papers
  • Includes supplementary material: sn.pub/extras

Part of the book series: Vector Optimization (VECTOROPT)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xxii
  2. Introduction

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 1-10
  3. Order Relations and Ordering Cones

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 11-76
  4. Continuity and Differentiability

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 77-108
  5. Tangent Cones and Tangent Sets

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 109-211
  6. Nonconvex Separation Theorems

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 213-248
  7. Hahn-Banach Type Theorems

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 249-273
  8. Conjugates and Subdifferentials

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 275-306
  9. Duality

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 307-348
  10. Existence Results for Minimal Points

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 349-368
  11. Ekeland Variational Principle

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 369-397
  12. Derivatives and Epiderivatives of Set-Valued Maps

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 399-508
  13. Optimality Conditions in Set-Valued Optimization

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 509-604
  14. Sensitivity Analysis in Set-Valued Optimization and Vector Variational Inequalities

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 605-643
  15. Numerical Methods for Solving Set-Valued Optimization Problems

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 645-661
  16. Applications

    • Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu
    Pages 663-725
  17. Back Matter

    Pages 727-765

About this book

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 economicsamong other things.

Reviews

“In this monograph, the first one entirely devoted to the subject, the authors present a unified treatment of the state of the art of most of the developments in this field. … It is very well written and contains numerous results and examples and over 600 references. … I wholeheartedly recommend this book to anyone interested in new trends in optimization, in particular, researchers who are interested in multiobjective/vector-optimization and its interconnection with variational analysis.” (Miguel Sama, Mathematical Reviews, December, 2015)

“The monograph contains a very large number of interesting, new or at least recent results not only in the fields of set-valued optimization together with many examples illustrating them. It is an interesting scientific resource for all researchers investigating problems of mathematical optimization.I can highly recommend it to graduate and PhD students as well as to scientists working in the fields of nonsmooth, multicriterial or set-valued optimization.” (S. Dempe, Optimization, July, 2015)

“This massive and very well-written book will probably be for many years the primary reference in set-valued optimization, the area of optimization where the objective and/or constraint functions of the considered problems are set-valued maps. … this book will be a solid reference for everyone interested in set-valued optimization, be they graduate students or established scientists.” (Sorin-Mihai Grad, zbMATH 1308.49004, 2015)

Authors and Affiliations

  • Rochester Institute of Technology School of Mathematical Sciences, Rochester, USA

    Akhtar A. Khan

  • Halle, Germany

    Christiane Tammer

  • University "Al. I. Cuza" Iasi Faculty of Mathematics, Iasi, Romania

    Constantin Zălinescu

Bibliographic Information

Buy it now

Buying options

eBook USD 44.99 USD 84.99
47% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 59.99 USD 109.99
45% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 59.99 USD 109.99
45% discount 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