Solving the nonlinear complementarity problem with lower and upper bounds

In order to solve the nonlinear complementarity problem with lower and upper bounds, a simplicial variable dimension restart algorithm is introduced. The algorithm subdivides the set on which the problem is defined into simplices and generates from an arbitrarily chosen starting point a piecewise linear path of points leading to an approximate solution. When the accuracy is not sufficient the algorithm can be restarted at the approximate solution with a finer simplicial subdivision. The piecewise linear path generated by the algorithm is followed by a sequence of adjacent simplices of varying dimension. The path can be interpreted as the path of solutions of the nonlinear complementarity problem with parametrized bounds.

Kremers, Johannes and Dolf Talman (1990), Solving the nonlinear complementarity problem with lower and upper bounds, Methods of Operations Research 60 , 407-417