Global convergence in a modified RMIL-type conjugate gradient algorithm for nonlinear systems of equations and signal recovery

This paper proposes a modified Rivaie-Mohd-Ismail-Leong (RMIL)-type conjugate gradient algorithm for solving nonlinear systems of equations with convex constraints. The proposed algorithm offers several key characteristics: (1) The modified conjugate parameter is non-negative, thereby enhancing the proposed algorithm's stability. (2) The search direction satisfies sufficient descent and trust region properties without relying on any line search technique. (3) The global convergence of the proposed algorithm is established under general assumptions without requiring the Lipschitz continuity condition for nonlinear systems of equations. (4) Numerical experiments indicated that the proposed algorithm surpasses existing similar algorithms in both efficiency and stability, particularly when applied to large scale nonlinear systems of equations and signal recovery problems in compressed sensing.