THE STRUCTURE OF THE EFFICIENT SOLUTIONS SET - THE

CONVEX CASE by Višnja Vojvodić-Rosenzweig, Zagreb, Croatia

Abstract. We prove two theorems on vector convex optimization, under appropriate assumptions of compactness. The first theorem, of technical nature, entails the existence of a special decomposition of variables in efficient solutions ‘intermediate’ between two known ones, an efficient and a proper efficient solution. The second theorem constructs a function which attains its unique minimum in any proper efficient solution. Mathematics subject classification: 46B40, 90C29, 90C31. Keywords: vector optimization, efficient point, proper efficient point, strictly quasiconvex function, strict norm.