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.
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Ioffe, A. A Lagrange multiplier rule with small convex-valued subdifferentials for nonsmooth problems of mathematical programming involving equality and nonfunctional constraints. Mathematical Programming 58, 137–145 (1993). https://doi.org/10.1007/BF01581262
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DOI: https://doi.org/10.1007/BF01581262