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 ...

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.

We present a new adaptive algorithm for convex quadratic multicriteria optimization. The algorithm is able to adaptively refine the approximation to the set of efficient points by way of a warm-start interior-point scalarization approach. Numerical results show that this technique is faster than a standard method used for this problem.

Scalarization approaches to purposely generating epsilon-efficient solutions of multiobjective programs are investigated and a generic procedure for computing these solutions is proposed and illustrated with an example. Real-life decision making situations in which the solutions are of significance are described.

The weighted sum method of vector objective scalarization is known to generate points on convex Pareto front whose distribution cannot be controlled. This work presents a method of improving the distribution of Pareto points generated by weighted sum method by nonlinear weight selection. Numerical examples are presented to show the effectiveness of the method.

The training phase is the most crucial stage during machine learning process. In case of labeled data and supervised learning, entails minimizing loss function under various constraints. We provide an innovative model for with numerous sets, resulting from application multicriteria optimization techniques to existing deep algorithms. Data fitting formulated as a in which each criterion measures...

In this work, we generalize the spontaneous scalarization phenomena in Einstein-Maxwell-scalar models to a higher spin field. The result is an Einstein-Maxwell-vector model wherein vector field nonminimally coupled Maxwell invariant by exponential coupling function. We show that latter guarantees circumvention of associated no-hair theorem when has form electric Different than its scalar counte...