Nonsmooth optimum problems with constraints

ZS Pales, V. M. Zeidan

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43 Citations (Scopus)


This paper develops second-order necessary conditions for nonsmooth infinite-dimensional optimization problems with Banach space-valued equality and real-valued inequality constraints. Another constraint in the form of a closed convex set is also present. The objective function is the maximum over a parameter of functions f(t, z) that are Lipschitz in z and upper semicontinuous in t. The inequality constraints g(s, z) depend on a parameter s. The technique we use is a generalization of that of Dubovitskii and Milyutin. The second-order conditions obtained here are in terms of a certain function σ that disappears when the parameters and a certain set that derives from the given convex set are absent. The presence of the function σ and that set is due to the envelope-like effect discovered by Kawasaki.

Original languageEnglish
Pages (from-to)1476-1502
Number of pages27
JournalSIAM Journal on Control and Optimization
Issue number5
Publication statusPublished - Jan 1 1994


ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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