 
Summary: Solving complementarity problems by means of a
new smooth constrained nonlinear solver
Roberto Andreani \Lambda Jos'e Mario Mart'inez y
October 17, 1997 (revised)
Abstract
Given F : IR n ! IR m
and\Omega a closed and convex set, the prob
lem of finding x 2 IR n such that x
2\Omega and F (x) = 0 is considered.
For solving this problem an algorithm of InexactNewton type is de
fined. Global and local convergence proofs are presented. As a prac
tical application, the Horizontal Nonlinear Complementarity Problem
is introduced. It is shown that the InexactNewton algorithm can be
applied to this problem. Numerical experiments are performed and
commented.
Keywords. Nonlinear systems, InexactNewton method, global con
vergence, convex constraints, box constraints, complementarity.
AMS: 65H10, 90C33, 90C30
\Lambda Department of Applied Mathematics, IMECCUNICAMP, University of Campinas,
CP 6065, 13081970 Campinas SP, Brazil . This author was supported by FAPESP (Grant
