A Dai-Liao-type projection method for monotone nonlinear equations and signal processing

Abstract

In this article, inspired by the projection technique of Solodov and Svaiter, we exploit the simple structure, low memory requirement, and good convergence properties of the mixed conjugate gradient method of Stanimirović et al. [New hybrid conjugate gradient and broyden-fletcher-goldfarbshanno conjugate gradient methods, J. Optim. Theory Appl. 178 (2018), no. 3, 860–884] for unconstrained optimization problems to solve convex constrained monotone nonlinear equations. The proposed method does not require Jacobian information. Under monotonicity and Lipschitz continuity assumptions, the global convergence properties of the proposed method are established. Computational experiments indicate that the proposed method is computationally efficient. Furthermore, the proposed method is applied to solve the ℓ1{\ell }_{1}-norm regularized problems to decode sparse signals and images in compressive sensing.

Keywords

• nonlinear equations
• unconstrained optimization
• conjugate gradient method
• projection method
• compressive sensing
• 90c30
• 65k05
• 90c53
• 49m37
• 15a18