A solution method for nonlinear monotone equations via hybrid spectral conjugate gradient and signal recovery problems

Abstract In this paper, we propose a solution method via hybrid spectral conjugate gradient and signal recovery problem (ANHSCG) to solve nonlinear monotone equations. This has been done using the hybrid conjugate gradient (CG) parameters of Dai-Yuan (DY), conjugate descent (CD), Hestenes-Stiefel (HS), Liu-Storey (LS) and the corresponding search direction of spectral conjugate gradient method. The search direction has proved to be adequately descent regardless of the step-size. Under reasonable assumptions, the convergence of the algorithm is established. Additionally, numerical tests are run on a set of benchmark test problems to illustrate the effectiveness and competitiveness of the new algorithm compared with other existing alternatives. Finally, some applications of the proposed algorithm is explored. Mathematics Subject Classification: 65K05, 90C52, 90C26