New three-term conjugate gradient algorithm for solving monotone nonlinear equations and signal recovery problems

Abstract

This work presents a new three-term projection algorithm for solving nonlinear monotone equations. The paper is aimed at constructing an efficient and competitive algorithm for finding approximate solutions of nonlinear monotone equations. This is based on a new choice of the conjugate gradient direction which satisfies the sufficient descent condition. The convergence of the algorithm is shown under Lipschitz continuity and monotonicity of the involved operator. Numerical experiments presented in the paper show that the algorithm needs a less number of iterations in comparison with existing algorithms. Furthermore, the proposed algorithm is applied to solve signal recovery problems.