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Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems
Authors:A Ben-Tal  J Zowe
Institution:(1) Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, Haifa, Israel;(2) Department of Mathematics, University of Bayreuth, 8580 Bayreuth, Germany
Abstract: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.
Keywords:Necessary and Sufficient Second Order Conditions  Nonsmooth Optimization  Minimax Problem  l 1-Approximation  Penalty Functions  Directional Derivatives
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