A Lagrange multiplier rule with small convex-valued subdifferentials for nonsmooth problems of mathematical programming involving equality and nonfunctional constraints期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Alexander Ioffe

Institution:	(1) Department of Mathematics, Technion — Israel Institute of Technology, 32000 Haifa, Israel

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

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