Document Type

Technical Report


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


Dedicated to Franco Giannessi in honor of his 75th birthday. This research was supported by the Australian Research Council under Discovery Grant DP0664423; and by the US National Science Foundation under Grant DMS-0603846.