A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing

Guodong Ma, Jiachen Jin, Jinbao Jian, Jianghua Yin, Dao-Lan Han

Abstract: In this paper, based on the three-term conjugate gradient projection method and the inertial technique, we propose a modified inertial three-term conjugate gradient projection method for solving nonlinear monotone equations with convex constraints. Embedding the inertial extrapolation step in the design for the search direction, the resulting direction satisfies the sufficient descent property which is independent of any line search rules. The global convergence and Q-linear convergence rate of the proposed algorithm are established under standard conditions. Numerical comparisons with three existing methods demonstrate that the proposed algorithm possesses superior numerical performance and good robustness for solving large-scale equations. Finally, the proposed method is applied to solve the sparse signal problems and image restoration in compressed sensing.