A Modified Integer Labeling for Complementarity Algorithms

Nonlinear complementary problems can be solved by algorithms based on the principle of simplicial approximation. We present such an algorithm that allows the choice of an arbitrary starting point without using an artificial labeling or an extra dimension. Furthermore the relation between the grid size of the triangulation and the accuracy of an approximate solution is investigated, and it is shown that a combination of the algorithm with Newton-steps yields better accuracy. Finally the algorithm is adapted for solving systems of equations.