A Hybrid Forward–Backward Algorithm and Its Optimization Application

Abstract

In this paper, we study a hybrid forward−backward algorithm for sparse reconstruction. Our algorithm involves descent, splitting and inertial ideas. Under suitable conditions on the algorithm parameters, we establish a strong convergence solution theorem in the framework of Hilbert spaces. Numerical experiments are also provided to illustrate the application in the field of signal processing.

Keywords

• forward–backward method
• hybrid steepest decent method
• inertial extrapolation
• maximally monotone
• strong convergence