Nonsmooth optimum problems with constraints

Z. Páles, V. M. Zeidan

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

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
Volume32
Issue number5
Publication statusPublished - Sep 1994

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Inequality Constraints
Convex Sets
Second-order Necessary Conditions
Second-order Conditions
Upper Semicontinuous
Closed set
Envelope
Lipschitz
Equality
Banach spaces
Objective function
Banach space
Optimization Problem
Generalization
Form

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Control and Optimization

Cite this

Nonsmooth optimum problems with constraints. / Páles, Z.; Zeidan, V. M.

In: SIAM Journal on Control and Optimization, Vol. 32, No. 5, 09.1994, p. 1476-1502.

Research output: Contribution to journalArticle

Páles, Z. ; Zeidan, V. M. / Nonsmooth optimum problems with constraints. In: SIAM Journal on Control and Optimization. 1994 ; Vol. 32, No. 5. pp. 1476-1502.
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