An overall study of convergence conditions for algorithms in nonlinear programming

Since the point-to-set maps were introduced by Zangwill^1] in the study of conceptual algorithms, various sufficient conditions for the algorithms to be of global convergence have been established. In this paper, the relations among all these conditions are illustrated by a unified approach; still more, unlike the sufficient conditions previously given in the literature, a new necessary condition is put forward at the end of the paper, so that it implies more applications.