Projective EAOR Algorithms For The Solutions Of Linear Complementarity Problems And Two-sided Obstacle Problems

Complementarity problems and two-sided obstacle problems can be met in the mathematical modellings of various applications in physics, mechanics, economics, operations research, optimal control theory and traffic assignment problems, etc. So it is significant to establish some efficient numerical methods to solving these problems. There have been lots of researches on the solutions of these problems, which presented feasible and essential techniques. In this paper, we discuss and analyze projective extrapolated accelerated overrelaxation iteration ( EAOR ) methods for solving linear complementarity problems and affine two-sided obstacle problems.At first, we give a review of a lot of achievements about projective iteration methods to solve complementarity problems, such as, projective relaxation iteration schemes and their theories. Then, we analyze nonlinear accelerated overrelaxation iteration methods to solve linear equation, which is better than classical relaxation iterates. The reason is that it has two relaxation factors, which can be chosen properly to accelerate the iteration process. In this paper, we will extend EAOR method to solve symmetric and copositive linear complementarity problems. We will establish projective EAOR method and show that any accumulation point of the interation generated by the method solves the linear complementarity problem. When the matrix A involved in the linear complementarity problem is a symmetric and copositive plus matrix or a symmetric and strictly copositive matrix, the sequence generated by the method exists an accumulation point which solves the linear complementarity problem. Moreover, when A is a nondegenerate, symmetric and copositive plus matrix, the sequence converges to a solution of the problem. Numerical experiment tests are presented to verify the theoretical results we obtained.On the other hand, we also discuss projective EAOR method to solve affine two-sided obstacle problem. Since linear complementarity problem and two-sided obstacle problem have a similar structure, especially when they are discribled by projective forms, similar theoretical results are obtained. Numerical experiments are also given.