A Novel Two-Step Inertial Viscosity Algorithm for Bilevel Optimization Problems Applied to Image Recovery

Abstract

This paper introduces a novel two-step inertial algorithm for locating a common fixed point of a countable family of nonexpansive mappings. We establish strong convergence properties of the proposed method under mild conditions and employ it to solve convex bilevel optimization problems. The method is further applied to the image recovery problem. Our numerical experiments show that the proposed method achieves faster convergence than other related methods in the literature.

Keywords

• convex bilevel optimization
• forward–backward algorithms
• image restoration problems
• two-step inertial
• viscosity approximation