In this paper we deal with a Fritz John type constrained vector optimization problem. In spite that there are many concepts of solutions for an unconstrained vector optimization problem, we show the possibility “to double” the number of concepts when a constrained problem is considered. In...

In this paper we deal with a Fritz John type constrained vector optimization problem. In spite that there are many concepts of solutions for an unconstrained vector optimization problem, we show the possibility “to double” the number of concepts when a constrained problem is considered. In...

Let E be a linear space, K E and f : K ? R. We put in terms of the lower Dini directional derivative a problem, referred to as GMV I(f ,K), which can be considered as a generalization of the Minty variational inequality of differential type (for short, MV I(f ,K)). We investigate, in the case of...

Minty Variational Inequalities (for short, MVI) have proved to characterize a kind of equilibrium more qualified than Stampacchia Variational Inequalities (for short, SVI). This conclusion leads to argue that, when a MVI admits a solution and the operator F admits a primitive minimization...

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...