EXISTENCE THEOREM OF CONE SADDLE-POINTS APPLYING A NONLINEAR SCALARIZATION

Abstract

This paper is concerned with a nonlinear scalarization for vectorvalued functions. We consider applying the scalarization to existence of cone saddle-points. Some properties of the scalarization about cone-continuity and cone-convexity are described and then as an application, an existence theorem for vector saddle-points is treated.