On Variational Principles, Level Sets, Well-Posedness, and ε-Solutions in Vector Optimization

D. Dentcheva, S. Helbig

Research output: Contribution to journalArticlepeer-review

59 Scopus citations

Abstract

Using the concept for ε-efficient solutions introduced in Refs. 1 and 2, we extend the Ekeland variational principle and another variational principle given in Ref. 3 to vector-valued objective functions. This enables us to establish a kind of well-posedness for the resulting perturbed vector optimization problems. Based on this definition of ε-efficiency, we also formulate a concept for level sets and prove some results about the Kuratowski limits of level sets.

Original languageEnglish
Pages (from-to)325-349
Number of pages25
JournalJournal of Optimization Theory and Applications
Volume89
Issue number2
DOIs
StatePublished - May 1996

Keywords

  • Nonlinear vector optimization
  • Variational principles
  • Well-posedness

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