Enhanced Dai–Liao conjugate gradient methods for systems of monotone nonlinear equations

In this paper, we propose two conjugate gradient methods for solving large-scale monotone nonlinear equations. The methods are developed by combining the hyperplane projection method by Solodov and Svaiter (Reformulation: nonsmooth, piecewise smooth, semismooth and smoothing methods. Springer, pp 355–369, 1998) and two modified search directions of the famous Dai and Liao (Appl Math Optim 43(1): 87–101, 2001) method. It is shown that the...