Abstract
It is shown that a Lagrange multiplier rule involving the Michel-Penot subdifferentials is valid for the problem: minimizef0(x) subject tofi(x) ⩽ 0,i = 1, ⋯,m;fi(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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