A generalized proximal point algorithm for the nonlinear complementarity problem

Abstract

We consider a generalized proximal point method (GPPA) for solving the nonlinear complementarity problem with monotone operators in R' lt differs from the classical proximal point method discussed by Rockafellar for the problem offinding zeroes of monotone operators in the use of generalized distances, called (p-divergences, instead of the Euclidean one. These distances play not only a regularization wie but also a penalization one, forcing the sequence generaled by the method to remain in the interior of the feasible set, so that the method behaves like an interior point one. Under appropriate assumptions on the ip-divergence and the monotone operator we prove that the sequence converges if and only if the problem has solutions, in which case the limit is a solution. If the problem does not have solutions, then the sequence is unbounded. We extend previous results for the proximal point method concerning convex optimization problems.