Distributed Optimization Method Based On Optimal Control

TL;DR

This paper introduces a novel distributed optimization framework that transforms the problem into an optimal control setting, leveraging maximum principle results to achieve convergence with superlinear rates.

Contribution

It presents a new distributed optimization algorithm based on optimal control and maximum principle, with rigorous convergence and superlinear rate analysis.

Findings

The proposed method converges globally.

Achieves superlinear convergence rate.

Effective for multi-agent systems.

Abstract

In this paper, a novel distributed optimization framework has been proposed. The key idea is to convert optimization problems into optimal control problems where the objective of each agent is to design the current control input minimizing the original objective function of itself and updated size for the future time instant. Compared with the existing distributed optimization problem for optimizing a sum of convex objective functions corresponding to multiple agents, we present a distributed optimization algorithm for multi-agents system based on the results from the maximum principle. Moreover, the convergence and superlinear convergence rate are also analyzed stringently.