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Vector Optimization

Theory, Applications, and Extensions

  • Johannes Jahn

Table of contents

  1. Front Matter
    Pages i-xv
  2. Convex Analysis

    1. Front Matter
      Pages 1-2
    2. Johannes Jahn
      Pages 3-36
    3. Johannes Jahn
      Pages 37-59
    4. Johannes Jahn
      Pages 61-100
  3. Theory of Vector Optimization

    1. Front Matter
      Pages 101-102
    2. Johannes Jahn
      Pages 103-114
    3. Johannes Jahn
      Pages 115-148
    4. Johannes Jahn
      Pages 149-160
    5. Johannes Jahn
      Pages 161-188
    6. Johannes Jahn
      Pages 189-207
  4. Mathematical Applications

    1. Front Matter
      Pages 209-210
    2. Johannes Jahn
      Pages 211-242
    3. Johannes Jahn
      Pages 243-278
  5. Engineering Applications

    1. Front Matter
      Pages 279-280
    2. Johannes Jahn
      Pages 315-349
    3. Johannes Jahn
      Pages 351-381
  6. Extensions to Set Optimization

    1. Front Matter
      Pages 383-384
    2. Johannes Jahn
      Pages 393-409
    3. Johannes Jahn
      Pages 411-421
    4. Johannes Jahn
      Pages 423-447
  7. Back Matter
    Pages 449-481

About this book

Introduction

This book presents fundamentals and important results of vector optimization in a general setting. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning.

This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.

Authors and affiliations

  • Johannes Jahn
    • 1
  1. 1.Naturwissenschaftl. Fakultät, Inst. Angewandte MathematikUniversität Erlangen-NürnbergErlangenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-17005-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Business and Economics
  • Print ISBN 978-3-642-17004-1
  • Online ISBN 978-3-642-17005-8
  • Buy this book on publisher's site