A three-term CGPM-based algorithm without Lipschitz continuity for constrained nonlinear monotone equations with applications

In this work, a new three-term conjugate gradient projection method (CGPM) with a new adaptive line search strategy is proposed for solving the large-scale nonlinear monotone equations with convex constraints. The proposed three-term CGPM-based algorithm has the following characteristics: (i) its search direction satisfies the sufficient descent and trust region properties which is independent of the line search; (ii) the nonlinear equations only satisfy continuous and monotone properties; (iii) its global convergence is analyzed and obtained without the Lipschitz continuity. Some preliminary numerical experiment results are reported and their corresponding performance profiles are illustrated, which show that the proposed algorithm is effective. Finally, the proposed algorithm is extended to solve sparse signal restoration problems.