Distributed Difference of Convex Optimization

• URL: http://arxiv.org/abs/2407.16728v1
• Date: Tue, 23 Jul 2024 14:41:32 GMT
• Title: Distributed Difference of Convex Optimization
• Authors: Vivek Khatana, Murti V. Salapaka,
• Abstract summary: A class of distributed problems involvingn$ agents with the local objective function at every agenti by the difference of the difference of $-difference on $-f_i$ and $-f_i$ are presented. The DDC-Consensus algorithm is developed to solve the non-regularized distributed squares problem.
• Score: 1.2661010067882734
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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