Bounded sets of Lagrange multipliers for vector optimization problems in infinite dimension

AbstractThe aim of this paper is to point out some sufficient constraint qualification conditions ensuring the boundedness of a set of Lagrange multipliers for vectorial optimization problems in infinite dimension. In some (smooth) cases these conditions turn out to be necessary for the existence of multipliers as well

Martin-Luther-Universität Halle-Wittenberg Institut für Mathematik Relations Between Strictly Robust Optimization Problems and a Nonlinear Scalarization Method Relations Between Strictly Robust Optimization Problems and a Nonlinear Scalarization Method Re

Abstract. We study a strictly robust optimization problem in the context of a nonlinear scalarization method. We introduce a strictly robust multicriteria optimization problem and discuss its relation to a well-known scalar strictly robust optimization problem by using the nonlinear scalarization concept. Furthermore, we propose an unrestricted multicriteria optimization problem and note that its set of weakly Pareto optimal solutions contains all solutions of the scalar strictly robust optimization problem