Second-order necessary conditions in locally Lipschitz optimization with inequality constraints
type: Item
instance of: scholarly article
title: Second-order necessary conditions in locally Lipschitz optimization with inequality constraints
zbMATH Open document ID: 1318.49026
author: E. Constantin
published in: Optimization Letters
publication date: 2015-03-23T00:00:00Z
review text: The author studies a nonsmooth scalar optimization problem involving finitely many inequality constraints. Primal necessary optimality conditions in terms of second-order directional derivatives are derived in the case that the objective function and active constraints are locally Lipschitz at the extremum point. Dual necessary optimality conditions via second-order directional derivatives are established in the case that the objective function and active constraints are locally Lipschitz, regular in the sense of Clarke and Gâteaux differentiable at the extremum point. The results obtained here are generalizations of some recent results by I. Ginchev and V. I. Ivanov.
reviewed by: Do Van Luu
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 49K27
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 6418510
zbMATH Keywords: nonsmooth optimization
zbMATH Keywords: isolated local minimizer
zbMATH Keywords: necessary optimality conditions
zbMATH Keywords: second-order directional derivatives
zbMATH Keywords: Clarke's generalized derivative
zbMATH Keywords: locally Lipschitz functions
MaRDI profile type: Publication
full work available at URL: s11590-014-0725-y
OpenAlex ID: W2006349151
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DOI: 10.1007/S11590-014-0725-Y
description: scientific article; zbMATH DE number 6418510