This paper mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way we obtain first-order optimality conditions of both lower subdifferential and upper subdifferential types and then second-order conditions of three kinds involving, respectively, generalized second-order directional derivatives, graphical derivatives of first-order subdifferentials, and secondorder subdifferentials defined via coderivatives of first-order constructions.
Number in Series
Applied Mathematics | Mathematics
AMS Subject Classification
49J52, 49J53, 90C30, 90C26, 26A27
Eberhard, Andrew C. and Mordukhovich, Boris S., "First-Order and Second-Order Optimality Conditions for Nonsmooth Constrained Problems via Convolution Smoothing" (2010). Mathematics Research Reports. 74.