A smoothing conjugate gradient method for solving systems of nonsmooth equations

Many problems in real world are reduced to systems of nonsmooth equations and hence many researchers study numerical methods for solving systems of nonsmooth equations. As numerical methods for solving systems of nonsmooth equations, Newton-like methods are known as efficient numerical methods. However, these methods are not necessarily applied directly to large-scale problems, because these methods need to store matrices. In this paper, we propose a smoothing method which is based on the nonlinear conjugate gradient method and does not store any matrices for solving systems of nonsmooth equations. In addition, we prove the global convergence property of the proposed method under standard assumptions. Finally, we give some preliminary numerical results.