Stability in Mathematical Programming with Nondifferentiable Data

Abstract

We study the variation under perturbation of isolated local minimizers of a nonlinear and ondifferentiable optimization problem. For this we extend to the Lipschitzian case a fundamental result concerning regular points. Then we introduce the notion of lower second-order directional derivative, from which we obtain a second-order sufficiency theorem. These two results are finally used for obtaining bounds for the variations of some classes of isolated minimizers.