In this paper some new contractive operators on C (a,b) of IFS type are built. Inverse problems are introduced and studied by convex optimization problems. A stability result and some optimality conditions are given.

In this work we provide a characterization of Ck,1 functions on Rn (that ik K times differentiable with locally Lipschitz k-th derivatives) by means of (k+1)-th divided differences and Riemann derivatives. In particular we prove that the class of Ck,1 functions is equivalent to the class of...

In this note a mean value theorem for continuous vector functions is introduced by mollified derivatives and smooth approximations

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...

In this paper we survey some notions of generalized derivative for C 1,1 functions. Furthermore some optimality conditions and numerical methods for nonlinear minimization problems involving C1,1 data are studied.

Minty variational inequalities have proven to define a stronger notion of equilibrium than Stampacchia variational inequalities. This conclusion leads to argue that some regularity, e.g. convexity or generalized convexity, has to be implicit for any function that admits a solution of the...

In this paper we study several existing notions of well-posedness for vector optimization problems. We distinguish them into two classes and we establish the hierarchical structure of their relationships. Moreover, we relate vector well-posedness and well-posedness of an appropriate...

In this paper we investigate the links among generalized scalar variational inequalities of differential type, vector variational inequalities and vector optimization problems. The considered scalar variational inequalities are obtained through a nonlinear scalarization by means of the so called...

In this paper we extend to the vector case the notion of increasing along rays function. The proposed definition is given by means of a nonlinear scalarization through the so-called oriented distance function from a point to a set. We prove that the considered class of functions enjoys...

A constrained optimization problem with set-valued data is considered. Different kind of solutions are defined for such a problem. We recall weak minimizer, efficient minimizer and proper minimizer. The latter are defined in a way that embrace also the case when the ordering cone is not pointed....