Smoothing Quasi-Newton For P₀ Function Nonlinear Complementarity Problem

The complementarity problem is a class of important optimization problems, which have important applications in engineering, economics and traffic equilibrium. The research on it is always the hot spots in nonlinear and computational science. Many results have been achieved. Numerical methods of the P₀ function nonlinear complementarity problem are studied in this thesis.In this thesis, we propose a smoothing Quasi-Newton method for solving P₀ function nonlinear complementarity problem. The algorithm considered here is based on the smoothing symmetric perturbed Fischer-Burmeister function and makes use of the derivative-free line search rule. Its global convergence is proved when the solution set of P₀ function nonlinear complementarity problem is non-empty, bounded and F' is Lips-chitz continuous. The main feature of our global convergence results is that we do not assume a priori the level set is bounded.