An efficient three-term conjugate gradient-based algorithm involving spectral quotient for solving convex constrained monotone nonlinear equations with applications

In this paper, based on an adaptive three-term conjugate gradient method proposed by Anderi, we propose a three-term conjugate gradient method involving spectral quotient. The search direction satisfies sufficient descent property independent of any line search and the parameter in our method is determined by Dai–Liao conjugacy condition. By combining with projection technology, we obtain a three-term projection method to solve large-scale non-smooth monotone nonlinear equations with convex constraints. Under some mild assumptions, the global convergence and R-linear convergence rate are proved. Numerical results show that our method is competitive and efficient for solving large-scale monotone nonlinear equations with convex constraints. Furthermore, our algorithm is also applied to recover a sparse signal from incomplete and contaminated sampling measurements in compressed sensing, and obtain practical, robust performance in comparing with other algorithms.