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Mathematical Programming

, Volume 58, Issue 1–3, pp 137–145 | Cite as

A Lagrange multiplier rule with small convex-valued subdifferentials for nonsmooth problems of mathematical programming involving equality and nonfunctional constraints

  • Alexander Ioffe
Article

Abstract

It is shown that a Lagrange multiplier rule involving the Michel-Penot subdifferentials is valid for the problem: minimizef0(x) subject tof i (x) ⩽ 0,i = 1, ⋯,m;f i (x) = 0,i = m + 1,⋯,n;xQ where all functionsf are Lipschitz continuous andQ is a closed convex set. The proof is based on the theory of fans.

Key words

Lipschitz function subdifferential fan weak prederivative of a Lipschitz map controllability Lagrange multiplier rule 

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Copyright information

© The Mathematical Programming Society, Inc. 1993

Authors and Affiliations

  • Alexander Ioffe
    • 1
  1. 1.Department of MathematicsTechnion — Israel Institute of TechnologyHaifaIsrael

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