Department of Applied Mathematics & Physics, Kyoto Univiversity

Technical Report #99016 (August, 1999)

The Proximal Point Algorithm for the P_0 Complementarity Problem
by Nobuo Yamashita, Junji Imai and Masao Fukushima

In this paper we consider a proximal point algorithm (PPA) for solving the nonlinear complementarity problem (NCP) with a $P_0$ function. PPA was originally proposed by Martinet and further developed by Rockafellar for monotone variational inequalities and monotone operator problems. PPA is known to have nice convergence properties under mild conditions. However, until now, it has been applied mainly to monotone problems. In this paper, we propose a PPA for the NCP involving a $P_0$ function and establish its global convergence under appropriate conditions by using the Mountain Pass Theorem. Moreover, we give conditions under which it has a superlinear rate of convergence.