A separation theorem for nonlinear inverse images of convex sets

Sz Baják, Z. Páles

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper offers first- and higher-order necessary conditions for the local disjointness of a finite system of sets that are nonlinear inverse images of convex sets. The proof is based on the characterizations of α-admissible and α-tangent variations to nonlinear inverse images of convex sets and a necessary condition for the local disjointness in terms of these variations. As an application, the results are used to obtain first- and higher-order necessary conditions of optimality in constrained optimization problems.

Original languageEnglish
Pages (from-to)125-144
Number of pages20
JournalActa Mathematica Hungarica
Volume124
Issue number2
DOIs
Publication statusPublished - 2009

Fingerprint

Separation Theorem
Order Conditions
Convex Sets
Higher Order
First-order
Necessary Conditions
Necessary Conditions of Optimality
Constrained Optimization Problem
Tangent line

Keywords

  • Admissible variation
  • Dubovitskii-Milyutin separation theorem
  • Hahn-Banach separation theorem
  • Inverse images of convex sets
  • Tangent variation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A separation theorem for nonlinear inverse images of convex sets. / Baják, Sz; Páles, Z.

In: Acta Mathematica Hungarica, Vol. 124, No. 2, 2009, p. 125-144.

Research output: Contribution to journalArticle

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