Department of Applied Mathematics & Physics, Kyoto Univiversity
Technical Report #99017 (August, 1999)
Globally Convergent Broyden-like Methods for Semismooth Equations and Applications to VIP, NCP and MCP
by Donghui Li and Masao Fukushima
In this paper, we propose a general smoothing
Broyden-like quasi-Newton method for solving a class of nonsmooth
equations. Under appropriate conditions, the proposed method converges to
a solution of the equation globally and superlinearly. In particular,
the proposed method
provides the possibility of developing a
quasi-Newton method that enjoys
superlinear convergence even if strict complementarity fails to hld.
We pay particular attention to semismooth equations arising from
nonlinear complementarity problems, mixed complementarity problems and
variational inequality problems. We show that under certain conditions,
the related methods based on the
perturbed Fischer-Burmeister function,
Chen-Harker-Kanzow-Smale smoothing
function and Gabriel-Mor\'e class of
smoothing functions converge globally and superlinearly.