A stochastic coordinate descent inertial primal-dual algorithm for large-scale composite optimization

TL;DR

This paper introduces a stochastic coordinate descent inertial primal-dual algorithm for large-scale convex optimization problems, combining inertial techniques with coordinate updates to improve convergence.

Contribution

It develops a novel inertial primal-dual algorithm with stochastic coordinate descent and proves its convergence using an inertial Krasnosel'skii-Mann iteration framework.

Findings

Algorithm converges under certain conditions.

Effective for large-scale composite convex optimization.

Extends existing primal-dual methods with stochastic and inertial features.

Abstract

We consider an inertial primal-dual algorithm to compute the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a stochastic coordinate descent inertial primal-dual splitting algorithm. Moreover, in order to prove the convergence of the proposed inertial algorithm, we formulate first the inertial version of the randomized Krasnosel'skii-Mann iterations algorithm for approximating the set of fixed points of a nonexpansive operator and investigate its convergence properties. Then the convergence of stochastic coordinate descent inertial primal-dual splitting algorithm is derived by applying the inertial version of the randomized Krasnosel'skii-Mann iterations to the composition of the proximity operator.