The class of strongly semicontinuous functions is considered. For these functions the notion of mollified derivatives, introduced by Ermoliev, Norkin and Wets, 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
Second-order mollified derivatives and optimization / S.P. Crespi, D. La Torre, M. Rocca. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. SUPPLEMENTO. - ISSN 1592-9531. - 52:2(2003), pp. 251-262. [10.1007/BF02872232]
Second-order mollified derivatives and optimization
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 and Wets, 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
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