Complementarity problems in GAMS and the PATH solver

A fundamental mathematical problem is to find a solution to a square system of nonlinear equations. There are many methods to approach this problem, t he most famous of which is Newton's method. In this paper, we describe a ge neralization 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 d raw the examples in this paper from an economic background. Finally, some e xtensions of the modeling format and the solver are described. (C) 2000 Els evier Science B.V. All rights reserved. JEL classification: C63.