Interval Algorithm Of The Absolute Linear Complementarity Problem

Complementarity problem is an important problem in the field of operation research and computational mathematics, it has been widely applied in engineering, economics, and operation research. It is proposed by Cottle and Dantzig who is famous for operator and the founder of the mathematical programming. Since the complementarity problem has been put forward, it developed very fast and got the attention and the grace of many researchers. Especially, in recent 30 years, complementarity problem get many signifi-cant achievements in the aspect of theory and algorithm.In this paper, interval algorithm of the absolute linear complementary problem is studied by using the interval analysis theory combined with Moore, Miranda and Borsuk testing. Interval algorithm of the absolute linear complementary problem not only has the characteristics of global convergence, but also can get the optimal solution according to the need as well as ensure the error bounds which is small enough for the enclosing solution. The main content is divided into four parts as follows:The main content of the first part:we first give some relevant definitions and lem-mas, and then make detail demonstration of the research significance and present situation of the absolute linear complementarity problem.The main content of the second part:by establishing the equivalent form of the absolute linear complementarity problem, we proved the existence and the uniqueness of the problem solution using Moore test.The main content of the third part:we take Miranda and Borsuk theorem as a tool to prove the existence of the solution, give some equivalent conditions of theorem and make a comparison of Moore、Miranda and Borsuk test, then we conclude the merits of the three tests when meet the problem.The main content of the forth part:we find the initial interval of the absolute linear complementarity problem, design the algorithm and prove the convergence of the abso-lute linear complementarity, give some numerical experiments and the result show the validity and reliability.Finally, we make a summary and further research at last.