Variational convexity of functions and variational sufficiency in optimization

Thời gian: 1630-17h30 ngày 13/7/2013

Địa điểm: Phòng 612, nhà A6

Tóm tắt: The talk is devoted to the study, characterizations, and applications of variational convexity of functions, the property that has been recently introduced by Rockafellar together with its strong counterpart. We establish several characterizations of variational and strong variational convexity of extended-real-valued functions in finite and infinite dimensions by showing, in particular, the equivalence of these variational properties to the conventional (local) convexity and strong convexity of its Moreau envelopes. Further characterizations of variational and strong variational convexity of functions are obtained via their second-order subdifferentials (generalized Hessians), which are coderivatives of subgradient mappings. We also study relationships of these notions with local minimizers and tilt-stable local minimizers. The obtained results are used for characterizing related notions of variational and strong variational sufficiency in composite optimization with applications to nonlinear programming.