On optimality conditions in nondifferentiable programming.

This paper is devoted to necessary optimality conditions in a mathematical programming problem without differentiability or convexity assumptions on the data. The main tool of this study is the concept of generalized gradient of a locally Lipschitz function (and more generally of a lower semi-continuous function). In the first part, we consider local extremization problems in the unconstrained case for objective functions taking values in (−∞, +∞]. In the second part, the constrained case is considered by the way of the cone of adherent displacements. In the presence of inequality constraints, we derive in the third part optimality conditions in the Kuhn-Tucker form under a constraint qualification. [ABSTRACT FROM AUTHOR]