In this paper we first develop two new results of variational analysis. One is a fixed point theorem for parametric dynamic systems in quasimetric spaces, which can also be interpreted as an existence theorem of minimal points with respect to reflexive and transitive preferences for sets in products spaces. The other one is a variational … Read more
In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, that the sequence generated by the method is well defined and converges globally to a Pareto-Clarke critical point. Our method may be seen as an extension, for … Read more
Filter networks are used as a powerful tool aimed at reducing the image processing time and maintaining high image quality. They are composed of sparse sub-filters whose high sparsity ensures fast image processing. The filter network design is related to solving a sparse optimization problem where a cardinality constraint bounds above the sparsity level. In … Read more
Our paper consists of two main parts. In the first one, we deal with the deterministic problem of minimizing a real valued function $f$ over the Pareto set associated with a deterministic convex bi-objective optimization problem (BOP), in the particular case where $f$ depends on the objectives of (BOP), i.e. we optimize over the Pareto … Read more
In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications it was started to develop a comprehensive theory for these vector optimization problems. Thereby also notions of proper efficiency … Read more
This paper develops a multiattribute preference ranking rule in the context of utility robustness. A nonparametric perturbation of a given additive reference utility function is specified to solve the problem of ambiguity and inconsistency in utility assessments, while preserving the additive structure and the decision maker’s risk preference under each criterion. A concept of robust … Read more
Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is important to have practical solution approaches for computing. In this work, we consider the inexact projected gradient-like method for … Read more
This paper develops some mathematical models arising in psychology and some other areas of behavioral sciences that are formalized via general preferences with variable ordering structures. Our considerations are based on the recent “variational rationality approach” that unifies numerous theories in different branches of behavioral sciences by using, in particular, worthwhile change and stay dynamics … Read more
Typical output from an optimization solver is a single optimal solution. At the same time, a set of high-quality and diverse solutions could be beneficial in a variety of contexts, for example problems involving imperfect information, or those for which the structure of high-quality solution vectors can reveal meaningful insights. In view of this, we … Read more
We introduce a new flexible Inexact-Restoration (IR) algorithm and an application to problems with multiobjective constraints (MOCP) under the weighted-sum scalarization approach. In IR methods each iteration has two phases. In the first phase one aims to improve the feasibility and, in the second phase, one minimizes a suitable objective function. This is done in … Read more