The Methods For Nonlinear Complementarity Problem Based On Penalty-free Technique

Complementary means that the problem is a problem to satisfy a complemen-tary relationship between the two decision variables and it contains substantiallycomplementary relationship reflects a relationship widespread. The nonlinear com-plementarity problem is complementary question the most widely used of a class, hasimportant theoretical and practical significance of its research solution. Commonnonlinear complementarity problem solution by some function, which was trans-formed into nonlinear equations or constrained optimization problems, and thenuse a smooth, non-smooth method or penalty function method to solve it. On thepractical application of these methods do not easily controlled, no penalty functionmethod based on recent proposed solution can be nonlinear complementarity prob-lems existing for further reform in order to achieve reduction in computation, whilethe algorithm is easy to implement purposes.This thesis includes three aspects: First, the use NCP function, transform filterright, proposed filter trust region method for solving nonlinear programming prob-lems; Second, given the filter algorithm good numerical results analysis of ideologi-cal filters, gives a more relaxed approach of non-monotone filter to make computingmore flexible; Third, further expansion of the study based on the contents of thesecond proposed for solving nonlinear complementarity problem without penaltyfunction also without filter approach. Under reasonable conditions, we give theglobal convergence of these algorithms, and numerical experiments.