A randomized intertial primal-dual fixed point algorithm for monotone inclusions

TL;DR

This paper introduces a randomized inertial primal-dual fixed point algorithm based on Nesterov's heavy ball method, designed for solving various monotone inclusion problems with convergence guarantees.

Contribution

It develops a novel inertial block-coordinate primal-dual algorithm with convergence analysis, extending to operator splitting methods for monotone inclusions and convex minimization.

Findings

Convergence of the proposed algorithm is rigorously established.

The method effectively handles large-scale monotone inclusion problems.

Extensions to composite problems demonstrate versatility.

Abstract

In this paper, we propose a randomized intertial block-coordinate primaldual fixed point algorithm to solve a wide array of monotone inclusion problems base on the modification of the heavy ball method of Nesterov. These methods rely on a sweep of blocks of variables which are activated at each iteration according to a random rule. To this end we formulate the inertial version of the Krasnosel'skii-Mann algorithm for approximating the set of fixed points of a quasinonexpansive operator, for which we also provide an exhaustive convergence analysis. As a by-product, we can obtain some intertial block-coordinate operator splitting methods for solving composite monotone inclusion and convex minimization problems.