Metrically Upper Semicontinuous Multifunctions and Their Intersections

摘要

We present a variety of methods for establishing metric upper semicontinuity. We give conditions for the intersection of metric upper semicontinuous multifunctions to be metric upper semicontinuous and discuss their applicability. The study of metric upper semicontinuity (stability) is of importance in optimization theory. The report discusses classical and recent techniques of establishing metric upper semicontinuity and provides their extensions. The metric upper semicontinuity of intersections, the importance of which has been recognized only recently, and several applications to optimization problems are discussed. (Author)