A general sufficiency theorem for nonsmooth nonlinear programming

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 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.