Distributed Difference of Convex Optimization

Autor:	Khatana, Vivek, Salapaka, Murti V.
Rok vydání:	2024
Předmět:	Mathematics - Optimization and Control Computer Science - Artificial Intelligence Computer Science - Distributed Parallel and Cluster Computing Electrical Engineering and Systems Science - Systems and Control
Druh dokumentu:	Working Paper
Popis:	In this article, we focus on solving a class of distributed optimization problems involving $n$ agents with the local objective function at every agent $i$ given by the difference of two convex functions $f_i$ and $g_i$ (difference-of-convex (DC) form), where $f_i$ and $g_i$ are potentially nonsmooth. The agents communicate via a directed graph containing $n$ nodes. We create smooth approximations of the functions $f_i$ and $g_i$ and develop a distributed algorithm utilizing the gradients of the smooth surrogates and a finite-time approximate consensus protocol. We term this algorithm as DDC-Consensus. The developed DDC-Consensus algorithm allows for non-symmetric directed graph topologies and can be synthesized distributively. We establish that the DDC-Consensus algorithm converges to a stationary point of the nonconvex distributed optimization problem. The performance of the DDC-Consensus algorithm is evaluated via a simulation study to solve a nonconvex DC-regularized distributed least squares problem. The numerical results corroborate the efficacy of the proposed algorithm. Comment: 9 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.16728 Zobrazit plný text záznamu View this record from Arxiv