GENERATION OF K−CONVEX TEST PROBLEMS IN VARIABLE ORDERING SETTINGS

Abstract

Vector optimization problem with variable ordering structure is an extension of classical VOP with applications in Medicine and Economy. An approach that has been extended to this class is the projected gradient method. Although its theoretical convergence has been obtained, numerical ex- perience is needed. In this work we propose two methods for generating test problems for this algorithm. Our proposals are based on Bishop-Phelps and simplicial cones respectively. In both cases we ensure that the hypothesis for the convergence of the projected gradient are satisfied.