An efficient projection algorithm for solving convex constrained monotone operator equations and sparse signal reconstruction problems

We propose an efficient three-term projection method for solving convex-constrained nonlinear monotone equations, with applications to sparse signal reconstruction problems, in this paper. The proposed algorithm has three main appealing features; it is a new variant of BFGS modification; it satisfies the famous D–L conjugacy condition, and it satisfies the sufficient descent condition. The global convergence of the proposed algorithm is proven under some suitable conditions. Numerical results presented display the efficacy of the proposed algorithm in comparison with existing algorithms. Finally, the proposed algorithm is used to solve the sparse signal reconstruction problem.