Optimality conditions for 2-regular problems with nonsmooth objective functions

A. V. Arutyunov, A. F. Izmailov, Ilya Shvartsman

Research output: Contribution to journalArticle

Abstract

For equality-constrained optimization problems with locally Lipschitzian objective functions, we derive meaningful first-order necessary conditions for local optimality without assuming conventional regularity of constraints. In the case of a smooth objective function, theories of optimality conditions of this kind have been developed in the last three decades. This work extends these results to the nonsmooth case, employing the generalized differentiation concepts of modern nonsmooth analysis. As a by-product of this development, we establish the upper estimate of the Mordukhovich subdifferential of the lower directional derivative. Some applications of these results to the problem of minimization of the maximum function and to the constrained version of a Steiner-type problem are discussed.

Original languageEnglish (US)
Pages (from-to)37-45
Number of pages9
JournalNonlinear Analysis, Theory, Methods and Applications
Volume90
DOIs
StatePublished - Jun 28 2013

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Nonsmooth Function
Optimality Conditions
Objective function
Lipschitzian Functions
Generalized Differentiation
Nonsmooth Analysis
Local Optimality
Directional derivative
Order Conditions
Subdifferential
Constrained Optimization Problem
Smooth function
Equality
Regularity
Constrained optimization
First-order
Necessary Conditions
Byproducts
Estimate
Derivatives

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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Optimality conditions for 2-regular problems with nonsmooth objective functions. / Arutyunov, A. V.; Izmailov, A. F.; Shvartsman, Ilya.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 90, 28.06.2013, p. 37-45.

Research output: Contribution to journalArticle

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