Newton's method for nonlinear inequalities

A Newton-type algorithm has been presented elsewhere for solving non-linear inequalities of the formf(x)0,g(x)=0, and quadratic convergence has been proved under very strong hypotheses. In this paper we show that the same results hold under a considerable weakening of the hypotheses.This research was supported in part by contract number N00014-67-A-0126-0015, NR 044-425, from the Office of Naval Research.