Pro Jected Gradient Methods for Ncp 57 Projected Gradient Methods for Nonlinear Complementarity Problems via Normal Maps

We present a new approach to solving nonlinear complementarity problems based on the normal map and adaptations of the projected gradient algorithm. We characterize a Gauss{Newton point for nonlinear complementarity problems and show that it is suucient to check at most two cells of the related normal manifold to determine such points. Our algorithm uses the projected gradient method on one cell and n rays to reduce the normed residual at the current point. Global convergence is shown under very weak assumptions using a property called nonstationary repulsion. A hybrid algorithm maintains global convergence, with quadratic local convergence under appropriate assumptions.