Based On The Research Of Ncp Function For Nonlinear Complementarity Problems

Nonlinear complementary problem is one of the important types ofvariation inequalities which have a wide application in economics, operationsresearch, engineering, cybernetics, transportation and many other fields. Inrecent years, more and more scholars are interested in the study of nonlinearcomplementary problems. This problem can be solved with the idea of changingnonlinear complementary problems into nonlinear equations or unconstrainedproblem. The bridge of transformation is the NCP function; therefore the studyof NCP function is necessary for the study of the nonlinear complementaryproblem. There are two types of NCP function, non-smooth NCP function andsmooth NCP function respectively.On the basis of the existing NCP function inductive analysis, the authorconstructed two NCP Function in this paper, non-smooth NCP function andsmooth NCP function. It yields a good l results by applying it to the nonlinearcomplementary problem.The non-smooth NCP function is applied to solving the nonlinearcomplementary problem, non-smooth NCP function is constructed on the basisof smooth approximation principle in Chapter Three, and in this chapter theauthor proves the nature of the non-smooth NCP function. The non-smooth NCPfunction is applied to convert the nonlinear complementary problems intononlinear equations, and then use smoothing Newton algorithm to solvenonlinear equations. Numerical experiments show the non-smooth NCPfunction is effective. Compared with the reference [15], the relatively highaccuracy of the results obtained, the relative error is relatively less.Another NCP function is constructed in this paper is smooth NCP function.On the basis of the traditional NCP function, the author explains the nature ofthe given smooth NCP function, and the relationship between traditional NCPfunction and constructed smooth NCP function. On the basis of this smoothNCP function, Merit functions apply its special properties; these properties areconducive for nonlinear complementary problem, which helps to make the nonlinear complementary problem into unconstrained optimization problems.The use of Derivative-Free descent algorithm for unconstrained optimizationproblems is effective to solve the nonlinear complementary problem. Undercertain conditions, it proves that the D-F decreased convergence is useful. Thealgorithm Numerical experiments show that the constructed smooth NCPfunction is effective, the calculation time is relatively short, and its superiorityof this function.