A Study On Semismooth Algorithm For Nonlinear Complementarity Problem

Semismooth Newton algorithms and modified Newton-type methods for solving non-linear complementarity problem by using several class of NCP-functions was proposed.The search direction of Semismooth Newton algorithms can generally be solved by theNewton equations, or by the Negative gradient directions. The methods has global con-vergence in proper conditions. Diferent examples of semismooth Newton algorithms arepresented. By the way, for the second particular class of one-parametric NCP-function, twomodified semismooth Newton method were proposed. We proofed that the first modifiedalgorithm is global convergent and the second modified algorithm is locally superlinearlyconvergent. At last, in the part of numerical experiments, examples of diferent algorithm-s are presented. The results show that the selection of parameter efect the experimentalresults greatly. Also, the method of parametric selection was analyzed.