%A Michael C. Ferris
%A Todd S. Munson
%T Complementarity Problems in GAMS and the PATH Solver
%D September 1998
%R 98-12
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X
A fundamental mathematical problem is to find a solution to
a square system of nonlinear equations. There are many methods to
approach this problem, the most famous of which is Newton's method.
In this paper, we describe a generalization of this problem, the
complementarity problem. We show how such problems are modeled
within the GAMS modeling language and provide details about the
PATH solver, a generalization of Newton's method, for finding
a solution. While the modeling format is applicable in many
disciplines, we draw the examples in this paper from an economic background.
Finally, some extensions of the modeling format and the solver are described.