%A Michael C. Ferris
%A Daniel Ralph
%T Projected Gradient Methods for Nonlinear Complementarity Problems via Normal Maps
%D June 1994, Revised November 1994
%R 94-08
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X
We present a new approach to solving nonlinear complementarity
problems based on the normal map and adaptations of the projected
gradient algorithm.
We characterize a Gauss--Newton point for nonlinear complementarity
problems and show that it is sufficient to check at most two cells
of the related normal manifold to determine such points.
Our algorithm uses the projected gradient method on one cell and $n$
rays to reduce the normed residual at the current
point. Global convergence is shown under very weak assumptions using
a property called nonstationary repulsion. A hybrid algorithm
maintains global convergence, with quadratic local convergence under
appropriate assumptions.