Distributed accelerated proximal conjugate gradient methods for multi-agent constrained optimization problems

TL;DR

This paper introduces two novel accelerated distributed algorithms for multi-agent constrained optimization, combining proximal, conjugate gradient, and Halpern methods to improve efficiency in solving complex problems.

Contribution

The paper presents new inertial accelerated distributed algorithms that leverage the structure of the problem for enhanced convergence in multi-agent settings.

Findings

Algorithms demonstrate faster convergence in numerical experiments.

Proximal conjugate gradient methods outperform traditional approaches.

Effective in handling large-scale multi-agent constrained problems.

Abstract

The purpose of this paper is to introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M number of smooth and M number of nonsmooth functions over the common fixed points of M number of nonlinear mappings. Exploiting the special properties of the cost component function of the objective function and the nonlinear mapping of the constraint problem of each agent, a new inertial accelerated incremental and parallel computing distributed algorithms will be presented based on the combinations of computations of proximal, conjugate gradient and Halpern methods. Some numerical experiments and comparisons are given to illustrate our results.