Mollified Derivatives and Second-Order Optimality Conditions
Mollified Derivatives and Second-Order Optimality Conditions
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.
- Università dell Insubria (Varese) Italy
- SKEMA BUSINESS SCHOOL France
- University of Insubria Italy
- University of Milan Italy
- Università Luigi Bocconi Italy
generalized differentiability, Smooth approximations ; Nonsmooth optimization ; Strong semicontinuity, Nonsmooth analysis, Optimality conditions and duality in mathematical programming, mollifiers, nonsmooth optimization
generalized differentiability, Smooth approximations ; Nonsmooth optimization ; Strong semicontinuity, Nonsmooth analysis, Optimality conditions and duality in mathematical programming, mollifiers, nonsmooth optimization
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