A SMOOTHING AND SCALING FLETCHER-REEVES TYPE CONJUGATE GRADIENT METHOD FOR SYSTEMS OF NONSMOOTH EQUATIONS

摘要

We propose a Fletcher-Reeves (FR) type conjugate gradient method for solving systems of nonsmooth equations. The proposed method is based on a smoothing technique and the scaling FR method given by Zhang, Zhou, and Li (2006). The generated search direction is a descent direction for the merit function and we do not need any matrix to compute the search direction. We give an algorithm of the proposed method with the Armijo line search condition and show its global convergence property. Finally, we provide some numerical results.