Global convergence of a predictor-corrector smoothing newton method for generalized nonlinear complementarity problem

Ke Su, Xiaoli Lu

COMPUTER MODELLING & NEW TECHNOLOGIES 2014 18(12A) 36-43

College of Mathematics and Computer Science, Hebei University, Baoding, 071002

A predictor-corrector smoothing Newton method for the generalized nonlinear complementarity problem is proposed based on a class of smoothing functions. Dislike the complementarity problem, there were more functions needed to be considered in generalized nonlinear complementarity problem (GNCP). Therefore, the first thing was to reformulate the GNCP to a system of smoothing equations. Then a predictor-corrector smoothing Newton algorithm was modified to solve the problem. Under some suitable con- ditions, the boundness of the iteration sequence generated by the proposed smoothing Newton method is proved. To describe the global convergent properties of the method, it shows that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem.