Mollified derivatives and second-order optimality conditions
G. Crespi
, , Matteo Rocca
2003, Journal of Nonlinear and Convex Analysis(3), pp.437-454
Résumé
The class of strongly semicontinuous functions is considered. For these functions the notion of mollified derivatives, introduced by Ermoliev, Norkin and Wets [8], is extended to the second order. By means of a generalized Taylor's formula, second order necessary and sufficient conditions are proved for both unconstrained and constrained optimization. Finally a characterization of convex functions is given