Computing solutions to generalized equilibrium models by successive under-relaxation

Generalized Equilibrium models typically consist of many thousands of simultaneous nonlinear equations. Computing the solution to such a system is non-trivial; however, surprisingly good results have been obtained using successive under-relaxation within Gauss-Seidel iterations. This paper presents some of the theoretical reasons why this method has been so reliable. Numerical results are presented on a moderate size test problem. Possibilities for more rapidly convergent algorithms are also presented.