Journal of Optimization Theory and Applications

, Volume 51, Issue 2, pp 205–241 | Cite as

A survey of vector optimization in infinite-dimensional spaces, part 2

  • J. P. Dauer
  • W. Stadler
Survey Paper

Abstract

The present survey deals with the state of vector optimization as a mathematical discipline. In this context, the optima are generally defined as maximal pointsy0 with respect to a partial order on the criteria space. The survey is restricted to a discussion of that literature which deals with pointsy0 which satisfy a maximality condition with respect toy0-comparable criteria values; papers which are based on a maximality condition satisfied for all admissible criteria values are included only in a supplementary bibliography. For the former, all aspects of the optimization process are surveyed, ranging from questions of existence to the treatment of duality. Particular attention is paid to questions of proper maximality. The discussion is based on a broad range of definitions and selected theorems from the literature.

Key Words

Survey papers vector maximum problems multicriteria optimization partially ordered vector spaces abstract optimization 

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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • J. P. Dauer
    • 1
  • W. Stadler
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of NebraskaLincoln
  2. 2.Division of EngineeringSan Francisco State UniversitySan Francisco

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