Optimality conditions for an exhausterable function on an exhausterable set

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Abstract

Exhausters are families of convex compact sets that allow one to represent directional derivative of the studied function at a point in the form of InfMax or SupMin of linear functions. Functions for which such a representation is valid we call exhausterable. This class of functions is quite wide and contains many nonsmooth ones. The set of exhausterable function is also called exhausterable. In the present paper we describe optimality conditions for an exhausterable function on an exhausterable set. These conditions can be used for solving many nondifferentiable optimization problems. An example that illustrate obtained results is provided.

Original languageEnglish
Pages (from-to)57-67
Number of pages11
JournalJournal of Global Optimization
Volume76
Issue number1
DOIs
StatePublished - 1 Jan 2020

Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics

Keywords

  • Constrained optimization
  • Exhausters
  • Nondifferentiable optimization
  • Nonsmooth analysis
  • Optimality conditions

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