On Quadratic Scalarization of One Class of Vector Optimization Problems in Banach Spaces

We study vector optimization problems in partially ordered Banach spaces and suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We discuss the so-called adaptive scalarization of such problems and show that the corresponding scalar nonlinear optimization problems can be by-turn approximated by quadratic minimization problems