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...

In this paper a notion of descent direction for a vector function defined on a box is introduced. This concept is based on an appropriate convex combination of the “projected” gradients of the components of the objective functions. The proposed approach does not involve an “apriori”...

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,...

We study a notion of well-posedness in vector optimization through the behaviour fo minimizing sequences of sets, defined in terms of Hausdorff set-convergence. We prove the involvement of strict efficiency, a refinement of the notion of efficiency, in the definition of well-posedness. Using 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...

This work establishes the lower convergence of the set of minimal points of An to the set of minimal points of A, whenever An is a sequence of convex subsets of an euclidean space satisfying the dominance property and converging to A. Using this result and introducing a property for a function f...

In this work we consider the critical points of a vector-valued function f. We study their stability in order to obtain a necessary condition for Paret efficiency. We point out, by an example, that the classical notions of stability (concerning a single point) are not suitable in the settings....

This paper addresses the problem of measuring the speed of adjustment of exchange rates and relative prices to purchasing power parity (PPP), in the multivariate context of Vector Autoregressive Processes (VAR). We consider the speed of adjustment of one variable y in response to another...