Second-order necessary and sufficient optimality conditions for minimizing a sup-type function

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Abstract

In this paper, we give second-order necessary and sufficient optimality conditions for a minimization problem of a sup-type function S(x)=sup{f(x, t);tε T}, where T is a compact set in a metric space and f is a function defined on ℝn ×T. Our conditions are stated in terms of the first and second derivatives of f(x, t) with respect to x, and involve an extra term besides the second derivative of the ordinary Lagrange function. The extra term is essential when {f(x, t)}t forms an envelope. We study the relationship between our results, Wetterling [14], and Hettich and Jongen [6].

Original languageEnglish
Pages (from-to)195-220
Number of pages26
JournalApplied Mathematics & Optimization
Volume26
Issue number2
DOIs
Publication statusPublished - Sep 1 1992

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

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