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Vector Variational Inequalities and Vector Optimization

Theory and Applications

  • Qamrul Hasan Ansari
  • Elisabeth Köbis
  • Jen-Chih Yao

Part of the Vector Optimization book series (VECTOROPT)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao
    Pages 1-78
  3. Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao
    Pages 79-142
  4. Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao
    Pages 143-180
  5. Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao
    Pages 181-222
  6. Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao
    Pages 223-264
  7. Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao
    Pages 265-273
  8. Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao
    Pages 275-297
  9. Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao
    Pages 299-338
  10. Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao
    Pages 339-427
  11. Qamrul Hasan Ansari, Elisabeth Köbis, Jen-Chih Yao
    Pages 429-485
  12. Back Matter
    Pages 487-509

About this book

Introduction

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

Keywords

vector optimization vector equilibrium problems set-valued maps Ekeland's variational principle sensitivity analysis existence theory well-posedness theory of variational inequalities theory of equlibrium problems

Authors and affiliations

  • Qamrul Hasan Ansari
    • 1
  • Elisabeth Köbis
    • 2
  • Jen-Chih Yao
    • 3
  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Institute of MathematicsMartin Luther University Halle-WittenbergHalleGermany
  3. 3.Center for General EducationChina Medical UniversityTaichungTaiwan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-63049-6
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Business and Management
  • Print ISBN 978-3-319-63048-9
  • Online ISBN 978-3-319-63049-6
  • Series Print ISSN 1867-8971
  • Series Online ISSN 1867-898X
  • Buy this book on publisher's site
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