Smoothing Algorithm For Nonlinear Complementarity Problems Based On NCP Function

The main content of this topic research as in the current society, the solving method in the mathematics can be of value in practice, based on the nonlinear direction makes a deep research in mathematics, with excellent academic achievements before, on top of that, the optimization and further exploration. As a whole is divided into five parts, this paper from the theorem of the development of the status quo of subject and the results of research both at home and abroad, for example, and according to certain algorithm is classified, the middle section of nonlinear complementary problem is optimized conditions for the solvability of get, finally summarized after promotion, the algorithm for the future development trend of a prospect, under the joint efforts of all the scholars constantly, there will be more solution has certain application in real life.This topic in applied mathematics involved in the specific solutions are constructed and nonlinear complementarity of NCP function combination, by assuming theory conversely prove our reasoning for complementarity problems is feasible, is a research value in practice. Based on the research, there have been many cases of FB function complementary problem to do the research and has successful applications, on the basis of the scalable, continue to further explore other solvability conditions, cross the homotopy equation and cases of foreign solution, implementation and construction, from the performance of the algorithm, operation complexity has carried on the contrast, can be seen to report the result of our optimization algorithm improves the performance and superiority.In the last part of this topic, to the algorithm and the solution after the revamp is summarized and review, found in a certain extent, there are still can continue to explore and in need of improvement. Especially the implicit function combined with complementary functions between again, after the integration may have larger optimization space. In the outlook for the future at the same time, put forward the alternative theorem of complementary problem, theoretically proved that the numerical results should be within the expected assessment, that is the direction of proof reasoning is correct and effective, is expected to later scholars can prove it for further research and the real application to the actual life and work, for the development of the society development was more space.Innovation of this paper is as follows:1. With the help of former scholars assume that results, the use of alternative theorems of complementary problem algorithm is optimized and discuss, the possibility of the existence conditions of solutions are obtained. 2. Use have proved that the NCP function theorem for the structure optimization of the homotopy equation, by making the actual propulsion and the optimization of algorithm improvement, get the homotopy method to the feasibility of complementary problem, use smooth NCP function approximation constructing homotopy equation, complementarity problems by homotopy method.