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Variable Ordering Structures in Vector Optimization

  • Gabriele Eichfelder

Part of the Vector Optimization book series (VECTOROPT)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Gabriele Eichfelder
    Pages 1-25
  3. Gabriele Eichfelder
    Pages 27-55
  4. Gabriele Eichfelder
    Pages 57-75
  5. Gabriele Eichfelder
    Pages 77-88
  6. Gabriele Eichfelder
    Pages 89-104
  7. Gabriele Eichfelder
    Pages 117-138
  8. Gabriele Eichfelder
    Pages 139-152
  9. Gabriele Eichfelder
    Pages 153-173
  10. Gabriele Eichfelder
    Pages 175-180
  11. Back Matter
    Pages 181-190

About this book

Introduction

This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vector-valued objective function where the elements in the objective space are compared based on a variable ordering structure: instead of a partial ordering defined by a convex cone, we see a whole family of convex cones, one attached to each element of the objective space.The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice.

Keywords

cone-valued maps duality linear scalarization nonlinear scalarization numerical methods optimality concepts

Authors and affiliations

  • Gabriele Eichfelder
    • 1
  1. 1.Institut für MathematikTechnische Universität IlmenauIlmenauGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-54283-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-54282-4
  • Online ISBN 978-3-642-54283-1
  • Series Print ISSN 1867-8971
  • Series Online ISSN 1867-898X
  • Buy this book on publisher's site