Department of Applied Mathematics & Physics, Kyoto Univiversity

Technical Report #99001 (February, 1999)

Smoothing Newton and Quasi-Newton Methods for Mixed Complementarity Problems
by Donghui Li and Masao Fukushima

The mixed complementarity problem can be
reformulated as a nonsmooth equation
by using the median operator. In this paper,
we first study some useful properties of
this reformulation and then
derive the Chen-Harker-Kanzow-Smale smoothing
function for the mixed complementarity problem.
On the basis of this smoothing function,
we present a smoothing Newton method
for solving the mixed complementarity problem.
The smoothing Newton method converges globally
if the problem involves a differentiable
$P_0$ function. Under suitable conditions,
the method exhibits a quadratic convergence
property. We also present a smoothing
Broyden-like method based on the same
smoothing function.
Under appropriate conditions,
the method converges globally and superlinearly.