A generalized proximal point algorithm for the nonlinear complementarity problem

We consider a generalized proximal point method (GPPA) for solving the nonl inear complementarity problem with monotone operators in R-n. It differs fr om the classical proximal point method discussed by Rockafellar for the pro blem of finding zeroes of monotone operators in the use of generalized dist ances, called phi-divergences, instead of the Euclidean one. These distance s play nor only a regularization role but also a penalization one, forcing the sequence generated by the method to remain in the interior of the feasi ble set, so that the method behaves like an interior point one. Under appro priate assumptions on the phi-divergence and the monotone operator we prove that the sequence converges if and only if the problem has solutions, in w hich case the limit is a solution. If the problem does nor have solutions, then the sequence is unbounded. We extend previous results for rile proxima l point method concerning convex optimization problems.