Image Convexity of Generalized Systems with Infinite-Dimensional Image and Applications

Convexity properties of a generalized system with infinite-dimensional image are investigated by means of the notions of image and its extensions associated with the system. Complete characterizations of (proper) linear separation in the image space are given by using the quasi-relative interior, which allow one to obtain necessary and/or sufficient conditions for the impossibility of an image convex generalized system with infinite- dimensional image. These new results are applied to investigate vector quasi-optimization problems and vector dynamic variational inequalities.