A general sufficiency theorem for nonsmooth nonlinear programming

Chaney, R. W.

doi:10.1090/S0002-9947-1983-0684505-9

A general sufficiency theorem for nonsmooth nonlinear programming
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Trans. Amer. Math. Soc. 276 (1983), 235-245 Request permission

Abstract:

Second-order conditions are given which are sufficient to guarantee that a given point be a local minimizer for a real-valued locally Lipschitzian function over a closed set in $n$-dimensional real Euclidean space. These conditions are expressed in terms of the generalized gradients of Clarke. The conditions provide a very general and unified framework into which many previous first- and second-order theorems fit.

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