In this paper some second order necessary and sufficient conditions are given for unconstrained and constrained optimization problems involving C^1 functions. A generalized derivative is obtained by approximation with smooth functions and it collapses to Clarke's definition when C^(1,1) data are...

In this paper second-order necessary optimality conditions for nonsmooth vector optimization problems are given by smooth approximations. We extend to the vector case the approach introduced by Ermoliev, Norkin and Wets to define generalized derivatives for discontinuous functions as limit of...

The class of strongly semicontinuous functions is considered. For these functionsthe notion of mollified derivatives, introduced by Ermoliev, Norkin andWets [8], is extended to the second order. By means of a generalized Taylor'sformula, second order necessary and sufficient conditions are...

Many definitions of second order generalized derivatives have been introduced to obtain optimality conditions for optimization problems involving C wedge(1,1)data. The aim of this paper is to show some relations among these definitions and to study necessary and sufficient optimality conditions...

The classical subdifferential calculus is a useful tool in order to estabilish characterizations of convex functions and optimality conditions; but it becomes usless when one thinks to study perturbed convex functions. In this paper by using Sobolev space theory we give some characterizations of...

In this paper we give new proofs of classical results wich establish that under certain hypotheses a function can be expressed almost everywhere as an indefinite repeated integral of its Riemann derivatives. These results were originally proved in the first half of the century and are...

The iterated function systems (IFS) are used in image processing theory; in particular they give a dynamic procedure of compression and decompression of computer images. In this paper we bulid an iterated function system on the space of distribution functions and we show how the inverse problem...

Many definitions of second-order generalized derivatives have been introduced to obtain optimality conditions for optimization problems with C wedge(1,1) data. The aim of this note is to show some relations among these definitions