Department of Applied Mathematics & Physics, Kyoto Univiversity
Technical Report #98016 (September, 1998)
Broyden-like Methods for Variational Inequality and Nonlinear
by Donghui Li and Masao Fukushima
In this paper, we propose a Broyden-like quasi-Newton method for solving
finite-dimensional variational inequality problems. By means of a perturbed
we successively approximate the KKT system for a variational inequality
problem by a sequence of smooth equations.
Based on these approximating equations, we present a Broyden-like method.
The method is well defined. We
show that under suitable conditions, the proposed method converges to
a KKT point of the variational inequality problem globally and superlinearly.
we show that when specialized to a nonlinear complementarity problem,
the proposed method converges globally
whenever the problem involves a $P_0$ function with Lipschitzian Jacobian.
Moreover, if the strict complementarity condition holds,
then the convergence rate is superlinear.