Radiality and semismoothness

Abstract

We provide sufficient conditions for radiality and semismoothness. In general Banach spaces, we show that calmness ensures Dini-radiality as well as Dini-convexity of solution set to inequality systems. In finite dimensional spaces, we introduce the concept of Clarke-radiality and semismoothness of order m and show that each subanalytic set satisfies these properties. Similar properties are obtained for locally Lipschitzian subanalytic functions