Smoothing Methods For The Generalized Complementarity Problems

The generalized nonlinear complementarity problems are the extension of the classical nonlinear complementarity problems. They are very important and useful in industrial and agricultural production. In this thesis, two smoothing methods are used to study the generalized nonlinear complementarity problems.Using a smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented. Based on this reformulation, two smoothing Newton methods are introduced for its solution.Under milder assumptions, we show that the two algorithms are su-perlinearly or Q-quadratically convergent.