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

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

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Article ID: iaor19941929
Country: Netherlands
Volume: 58
Issue: 1
Start Page Number: 137
End Page Number: 145
Publication Date: Jan 1993
Journal: Mathematical Programming (Series A)
Authors:
Keywords: programming: nonlinear
Abstract:

It is shown that a Lagrange multiplier rule involving the Michel-Penot subdifferentials is valid for the problem: minimize f0(x) subject to fi(x)•0, i=1,...,m; fi(x)=0, i=m+1,...,n; x∈Q where all functions f are Lipschitz continuous and Q is a closed convex set. The proof is based on the theory of fans.

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