In this paper we introduce notions of well-posedness for a vector optimization problem and for a vector variational inequality of differential type, we study their basic properties and we establish the links among them. The proposed concept of well-posedness for a vector optimization problem...

For a Fritz John type vector optimization problem with C0,1 data we define different type of solutions, give their scalar characterizations applying the so called oriented distance, and give necessary and sufficient first order optimality conditions in terms of the Dini derivative. While...

A class of scalarizations is studied in order to characterize weakly efficient, efficient and properly efficient points of a non convex vector problem.A parallelism is established between the different solutions of the scalarized problem and the various efficient frontiers.In particular,...

In this paper we introduce a generalized second-order Riemann-type derivative for C 1,1 vector functions and use it to establish necessary and sufficient optimality conditions for vector optimization problems. We show that these conditions are stronger than those obtained by means of the...

In vector optimization many notions of approximate solution have been proposed in the literature. In this paper an axiomatic approach is introduced in order to study the approximate solution map of a vector optimization problem in the image space. An impossibility result is proved in the sense...

We study the behaviour of the minimal sets of a sequence of convex sets An converging to a given set A. Under suitable assumptions involving only the structure of the single sets An, we obtain the lower convergence of MinAn to MinA. In a reflexive Banach space ordered by a closed convex cone...