An inertial three-operator splitting algorithm with applications to image inpainting

Abstract

The three-operators splitting algorithm is a popular operator splitting method for finding the zeros of the sum of three maximally monotone operators, with one of which is cocoercive operator. In this paper, we propose a class of inertial three-operator splitting algorithm. The convergence of the proposed algorithm is proved by applying the inertial Krasnoselskii-Mann iteration under certain conditions on the iterative parameters in real Hilbert spaces. As applications, we develop an inertial three-operator splitting algorithm to solve the convex minimization problem of the sum of three convex functions, where one of them is differentiable with Lipschitz continuous gradient. Finally, we conduct numerical experiments on a constrained image inpainting problem with nuclear norm regularization. Numerical results demonstrate the advantage of the proposed inertial three-operator splitting algorithms.

arXiv comment26 pages, 14 figures

References in corpus (7)

• An inertial forward-backward algorithm for monotone inclusions
• Generalized Forward-Backward Splitting
• The rate of convergence of Nesterov's accelerated forward-backward method is actually faster than $1/k^2$
• An inertial alternating direction method of multipliers
• A Three-Operator Splitting Scheme and its Optimization Applications
• A splitting primal-dual proximity algorithm for solving composite optimization problems
• A first-order splitting method for solving a large-scale composite convex optimization problem

Cited by in corpus (4)

• Convergence Analyses of Davis-Yin Splitting via Scaled Relative Graphs II: Convex Optimization Problems
• Inertial Three-Operator Splitting Method and Applications
• Convergence analysis of a relaxed inertial alternating minimization algorithm with applications
• Convergence analysis of an inexact inertial Krasnoselskii-Mann algorithm with applications