Mathematical Programming

, Volume 24, Issue 1, pp 70–91

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

  • A. Ben-Tal
  • J. Zowe

DOI: 10.1007/BF01585095

Cite this article as:
Ben-Tal, A. & Zowe, J. Mathematical Programming (1982) 24: 70. doi:10.1007/BF01585095


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 l1-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.

Key words

Necessary and Sufficient Second Order ConditionsNonsmooth OptimizationMinimax Probleml1-ApproximationPenalty FunctionsDirectional Derivatives

Copyright information

© The Mathematical Programming Society, Inc. 1982

Authors and Affiliations

  • A. Ben-Tal
    • 1
  • J. Zowe
    • 2
  1. 1.Faculty of Industrial Engineering and ManagementTechnion-Israel Institute of TechnologyHaifaIsrael
  2. 2.Department of MathematicsUniversity of BayreuthBayreuthGermany