A Multistep Spectral DY‐Type Projection Method With the Momentum Term for Nonlinear Equations and Its Application

ABSTRACT In this paper, we propose a multistep spectral DY‐type projection method to solve nonlinear equations with convex constraints, in which we utilize the momentum term to improve the computational performance. Based on the structure of the multistep curve method, the first direction is selected as the fastest descent direction, and the second direction is the modified search direction of the PDY method proposed by Liu and Feng. Global convergence is proved under some appropriate conditions. Moreover, the asymptotic and nonasymptotic global convergence rate of the proposed method is demonstrated. Numerical results show that the proposed method is effective for solving large‐scale nonlinear equations and the sparse signal recovery problem.