Simplicial approximation of solutions to the nonlinear complementarity problem with lower and upper bounds

Ideas of a simplicial variable dimension restart algorithm to approximate zero points onR ⁿ developed by the authors and of a linear complementarity problem pivoting algorithm are combined to an algorithm for solving the nonlinear complementarity problem with lower and upper bounds. The algorithm can be considered as a modification of the2n-ray zero point finding algorithm onR ⁿ . It appears that for the new algorithm the number of linear programming pivot steps is typically less than for the2n-ray algorithm applied to an equivalent zero point problem. This is caused by the fact that the algorithm utilizes the complementarity conditions on the variables. This work is part of the VF-program “Equilibrium and Disequilibrium in Demand and Supply,” which has been approved by the Netherlands Ministry of Education and Sciences.