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.