The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of subsets of the same space de…ned by means of vector-valued functions. These Farkas-type results are used to derive characterizations of the weak solutions of vector optimization problems (including ...

* Correspondence: jeky99@126. com; [email protected] School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, P.R. China Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea Full list of author information is available at the end of the article Abstract In this article, we consider a class of parametric generalized vector quas...

In this study, we address the regression problem on set-valued samples that appear in applications. To solve this problem, we propose a support vector regression approach for set-valued samples that generalizes the classical e-support vector regression. First, an initial representative point (or an element) for every set-valued sample is selected, and a weighted distance between the initial rep...

we study the equilibrium states for an energy functional with a parametric force field on a region of a surface. consideration of free equilibrium states is based on lyusternik - schnirelman's and skrypnik's variational methods. consideration of equilibrium states under a constraint of geometrical character is based on an analog of skrypnik's method, described in cite{vyr3}. in local coordinate...

We study optimal control problems with vector-valued controls. As model problem serves the optimal distributed control of the instationary Navier-Stokes equations. In the article, we propose a solution strategy to solve optimal control problems with pointwise convex control constraints. It involves a SQP-like step with an imbedded active-set algorithm. The efficiency of that method is demonstra...

In this paper, we consider a bilevel vector optimization problem where objective and constraints are set valued maps. Our approach consists of using a support function [1, 2, 3, 14, 15, 32] together with the convex separation principle for the study of necessary optimality conditions for D.C bilevel set valued optimization problems. We give optimality conditions in terms of the strong subdiffer...