The class of strongly semicontinuous functions is considered. For these functions the notion of mollified derivatives, introduced by Ermoliev, Norkin andWets [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
Mollified derivatives and second-order optimality conditions / G.P. Crespi, D. La Torre, M. Rocca. - In: JOURNAL OF NONLINEAR AND CONVEX ANALYSIS. - ISSN 1345-4773. - 4:3(2003), pp. 437-454.
Mollified derivatives and second-order optimality conditions
D. La TorreSecondo
;
2003
Abstract
The class of strongly semicontinuous functions is considered. For these functions the notion of mollified derivatives, introduced by Ermoliev, Norkin andWets [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
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