Characterizations of nonsmooth generalized polarly cone-monotone maps

Abstract

In this paper we consider different types of generalized cone-mono-tone maps: polarly C-monotone, strictly polarly C-monotone, strongly polarly C-monotone, polarly C-pseudomonotone, strictly polarly C-pseudomonotone and polarly C-quasimonotone maps, where C is a cone in a finite-dimensional space Rm. We characterize these maps in the case when they are radially continuous with respect to the positive polar cone C+ of the cone C, generalizing some well known results. In the obtained theorems we use first and higher-order lower Dini directional derivatives.