The Linear Complementarity Problem

Linear complementary problem is a cross-cutting area of operations research and computational mathematics, which has a wide range of important applications, such as, spatial price equilibrium, game theory model, contact mechanics, fracture mechanics, elastic-plastic problems, obstacles and free boundary problems, fluid elastic dynamic lubrication problem, optimal control problems and traffic balance.The most salient feature of this linear complementary problem is the complementary condition, that is, it requires the product of two non-negative vectors is zero.In this paper, an index iterative method is presented for solving the linear complementary problem with interval elements. For computing this linear complementary problem efficiently, a monotonic algorithm is designed in this paper. Numerical results suggest the algorithm will end after finite iteration counts.On the other hand, for extending the applications of the linear complementary problem, this paper has presented a class of new linear complementary problem, namely, complex linear complementary problem. Clearly, the linear complementary problem is a simple case of the complex linear complementary problem. For calculating this kind of linear complementary problem, a new algorithm is proposed in this paper, which can solve the error estimation problem. Numerical experiments illustrate the efficiency of this algorithm.Additionally, this paper has studied the determination method of the nonsingular H -matrix and given some sufficient conditions.