Improved Dai-Yuan iterative schemes for convex constrained monotone nonlinear systems

Two new Dai-Yuan (DY) iterative schemes are presented in this article for solving constrained system of nonlinear monotone equations. Using an extension of the classical scheme by Dai and Yuan [Soc. Ind. Appl. Math., 10(1)(1999) 177-182], two modified DY search directions are obtained, which possess the vital property for analyzing global convergence. By conducting eigenvalue analysis, appropriate values were obtained for the nonnegative parameter C of the two schemes. The self-restarting structure of the first scheme, as well as the choices of the parameter C in both methods, ensure fast convergence to the solution of the problems considered. Algorithms of both schemes are implemented by employing monotone line search procedure by Zhang and Zhou [J. Comput. Appl. Math. 196(2006) 478-484] and the projection technique. Using fundamental assumptions, global convergence of both schemes is established and results of numerical experiments with four recent methods in the literature show that the new methods are encouraging.