GLOBAL CONVERGENCE OF SMOOTHING AND SCALING PRP TYPE CONJUGATE GRADIENT METHOD FOR SYSTEM OF NONSMOOTH EQUATIONS

Abstract

This paper treats numerical methods to solve systems of nonsmooth equations. Such problems arise in solving variational inequality problems, complementarity problems and so forth. Although smoothing Newton methods are known as efficient methods for solving systems of nonsmooth equations, these cannot be applied directly to large-scale problems because of the storage of memories for matrices. On the other hand, particular attention is paid to conjugate gradient methods for solving large-scale unconstrained optimization problems, because they do not require the use of matrices.

In this paper, combining the smoothing technique and the PRP type scaling conjugate gradient method, we propose a smoothing and scaling conjugate gradient method which does not use any matrices. Moreover, we show its global convergence. Finally, some numerical results are given.