We consider scalarization issues for vector problems in the case where the preference relation is represented by a rather arbitrary set. An algorithm for weights choice for a priori unknown preference relations is suggested. Some examples of applications to vector optimization, game equilibrium, and variational inequalities are described. DOI: 10.3103/S1066369X12090022

Efficient points are obtained for cone-ordered maximizations in n R using the method of scalarization. Various scalarizations are presented for ordering cones in general and then for the important special case of polyhedral cones. For polyhedral cones, it is shown how to find vectors in the positive dual cone that are needed for a scalarized objective function. Instructive examples are presented.

The purpose of this paper is to consider the set-valued optimization problem in Asplund spaces without convexity assumption. By a scalarization function introduced by Tammer and Weidner (J Optim Theory Appl 67:297–320, 1990), we obtain the Lagrangian condition for approximate solutions on set-valued optimization problems in terms of the Mordukhovich coderivative.

In a stochastic and fuzzy environment, a multi-objective fuzzy stopping problem is discussed. The randomness and fuzziness are evaluated by probabilistic expectations and scalarization functions respectively. Pareto optimal fuzzy stopping times are given under the assumption of regularity for stopping rules, by using λ-optimal stopping times.

In this paper by using the scalarization method, we consider Stamppachia variational-like inequalities in terms of normal subdifferential for set-valued maps and study their relations with set-valued optimization problems. Furthermore, some characterizations of the solution sets of K-pseudoinvex extremum problems are given.

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 scalarization. This approach allows us to show that, under some compactness assumption, quasiconvex problems are ...

We obtain sufficient and/or necessary conditions for global/local error bounds for the distances to some sets appeared in set optimization studied with both the set approach and vector approach (sublevel sets, constraint sets, sets of all Pareto efficient/ Henig proper efficient/super efficient solutions, sets of solutions corresponding to one Pareto efficient/Henig proper efficient/super effic...

the main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for three self mappings in $b$-metric spaces. next, we obtain cone $b$-metric version of these results by using a scalarization function. our results extend and generalize several well known comparable results in the existing literature.

By exploiting recent results, it is shown that the theories of Vector Optimization and of Vector Variational Inequalities can be based on the image space analysis and theorems of the alternative or separation theorems. It is shown that, starting from such a general scheme, several theoretical aspects can be developed – like optimality conditions, duality, penalization – as well as methods of so...

We present some integrals for vector measurable multifunctions with respect to a fuzzy measure obtained by scalarization. Calculus rules, relationships between these integrals and the vector integrals defined until now and some convergence results are presented. Key–words: fuzzy measure, fuzzy integral, measurable multifunction.