Distributed Mirror Descent Algorithm with Bregman Damping for Nonsmooth Constrained Optimization

TL;DR

This paper introduces a novel distributed mirror descent algorithm with Bregman damping, enhancing efficiency in nonsmooth constrained optimization problems by leveraging mirror descent properties and rigorous convergence guarantees.

Contribution

It presents a new distributed mirror descent algorithm with Bregman damping, generalizing existing projection-based methods for nonsmooth constrained optimization.

Findings

Algorithm converges with proven guarantees.

Trajectory remains bounded during optimization.

Effective in solving nonsmooth constrained problems.

Abstract

To solve distributed optimization efficiently with various constraints and nonsmooth functions, we propose a distributed mirror descent algorithm with embedded Bregman damping, as a generalization of conventional distributed projection-based algorithms. In fact, our continuous-time algorithm well inherits good capabilities of mirror descent approaches to rapidly compute explicit solutions to the problems with some specific constraint structures. Moreover, we rigorously prove the convergence of our algorithm, along with the boundedness of the trajectory and the accuracy of the solution.