New proximal type algorithms for convex minimization and its application to image deblurring

Abstract

In this work, we are interested in solving a convex minimization problem in real Hilbert spaces. We propose a new modified proximal algorithm using the inertial extrapolation and the linesearch technique. Its weak convergence theorems are established under mild conditions. Numerical experiments are presented to illustrate the performance of the proposed algorithm in image deblurring.