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Vector Optimization with Infimum and Supremum

  • Book
  • © 2011

Overview

Authors:
  1. Andreas Löhne

    1. , NWF II - Institut für Mathematik, Martin-Luther-Universität Halle-Wittenbe, Halle (Saale), Germany

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  • Presents a completely new approach to Vector Optimization
  • Covers the range from theory to algorithms
  • Includes a self-contained chapter on the linear case
  • Includes supplementary material: sn.pub/extras

Part of the book series: Vector Optimization (VECTOROPT)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Andreas Löhne
    Pages 1-3

  3. General and Convex Problems

    1. Front Matter

      Pages 5-5
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    2. A complete lattice for vector optimization

      • Andreas Löhne
      Pages 7-42

    3. Solution concepts

      • Andreas Löhne
      Pages 43-74

    4. Duality

      • Andreas Löhne
      Pages 75-107

  4. Linear Problems

    1. Front Matter

      Pages 109-109
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    2. Solution concepts and duality

      • Andreas Löhne
      Pages 111-159

    3. Algorithms

      • Andreas Löhne
      Pages 161-195

  5. Back Matter

    Pages 197-206
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Keywords

About this book

The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.

Authors and Affiliations

  • , NWF II - Institut für Mathematik, Martin-Luther-Universität Halle-Wittenbe, Halle (Saale), Germany

    Andreas Löhne

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