Hybrid Forward-Backward Algorithms Using Linesearch Rule for Minimization Problem

Kunrada Kankam, Nattawut Pholasa, Prasit Cholamjiak

Abstract

In this work, we investigate strong convergence of the sequences generated by the forward-backward algorithms using hybrid projection method and shrinking projection method for solving the minimization problem. The main advantage of our algorithms is that the Lipschitz constants of the gradient of functions do not require in computation. Finally, we present numerical experiments of our algorithms which are defined by two kinds of projection methods to show the efficiency and the implementation for LASSO problem in signal recovery.