The question we address is how robust solutions react to changes in the uncertainty set. We prove the location of robust solutions with respect to the magnitude of a possible decrease in uncertainty, namely when the uncertainty set shrinks, and convergence of the sequence of robust solutions. In...

The question we address is how robust solutions react to changes in the uncertainty set. We prove the location of robust solutions with respect to the magnitude of a possible decrease in uncertainty, namely when the uncertainty set shrinks, and convergence of the sequence of robust solutions. In...

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...

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....

A a set-valued optimization problem minC F(x), x 2 X0, is considered, where X0 X, X and Y are Banach spaces, F : X0 Y is a set-valued function and C Y is a closed cone. The solutions of the set-valued problem are defined as pairs (x0, y0), y0 2 F(x0), and are called minimizers. In particular the...