Adaptive three-term family of conjugate residual methods for system of monotone nonlinear equations

Two new conjugate residual algorithms are presented and analyzed in this article. Specifically, the main functions in the system considered are continuous and monotone. The methods are adaptations of the scheme presented by Narushima et al. (SIAM J Optim 21: 212-230, 2011). By employing the famous conjugacy condition of Dai and Liao (Appl Math Optim 43(1): 87-101, 2001), two different search directions are obtained and combined with the projection technique. Apart from being suitable for solving smooth monotone nonlinear problems, the schemes are also ideal for non-smooth nonlinear problems. By employing basic conditions, global convergence of the schemes is established. Report of numerical experiments indicates that the methods are promising.