Two Kinds Of Matrix Splitting Iteration Methods For Nonlinear Implicit Complementary Problems

Complementarity problem is to find a variable or a function that satisfies a certain non-negative property and complementary relationship,which are common exists in our daily life.It not only has closely connect with nonlinear analysis,but also has been widely used in many fields,such as optimization theory,engineering,structural mechanics,elastic theory,lubrication theory,variational calculus,mathematical economic equilibrium theory,man-agement science,and stochastic optimal control and so on.So,complementary problem has been the attention of the general mathematical researchers and fans since it was introduced and researched.The theoretical achievements of complementary problem has been con-stantly enriched and developed through the untiring efforts of the mathematics researchers,which made the complementary problem become the most important part of Mathematical Programming a very important part of the mathematical programming,at the same time,the study of the algorithm were also constantly improved.In recent years,all kinds of iterative algorithm for complementarity problem that correspond to all kinds of practical problems have been put forward.In this paper,we will propose two matrix splitting iteration methods for solving non-linear implicit complementary problem,discuss the convergence condition when the coeffi-cient matrix are positive definite matrix or_+-matrix,and give the parameter scope under certain special circumstances.Finally,we will verify the effectiveness of the proposed iter-ative algorithm by numerical experiments.