Vector Optimization with Infimum and Supremum

  • Andreas Löhne

Part of the Vector Optimization book series (VECTOROPT)

Table of contents

  1. Front Matter
    Pages i-x
  2. Andreas Löhne
    Pages 1-3
  3. General and Convex Problems

    1. Front Matter
      Pages 5-5
    2. Andreas Löhne
      Pages 7-42
    3. Andreas Löhne
      Pages 43-74
    4. Andreas Löhne
      Pages 75-107
  4. Linear Problems

    1. Front Matter
      Pages 109-109
    2. Andreas Löhne
      Pages 111-159
    3. Andreas Löhne
      Pages 161-195
  5. Back Matter
    Pages 197-206

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.


complete lattice cutting plane methods duality multiobjective optimization self-infimal sets

Authors and affiliations

  • Andreas Löhne
    • 1
  1. 1., NWF II - Institut für MathematikMartin-Luther-Universität Halle-WittenbeHalle (Saale)Germany

Bibliographic information