, Volume 24, Issue 1, pp 70-91

Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems

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The purpose of this paper is to derive, in a unified way, second order necessary and sufficient optimality criteria, for four types of nonsmooth minimization problems: thediscrete minimax problem, thediscrete l 1-approximation, the minimization of theexact penalty function and the minimization of theclassical exterior penalty function. Our results correct and supplement conditions obtained by various authors in recent papers.