Fenchel Dual Gradient Methods for Distributed Convex Optimization over Time-varying Networks
Abstract
In the large collection of existing distributed algorithms for convex multi-agent optimization, only a handful of them provide convergence rate guarantees on agent networks with time-varying topologies, which, however, restrict the problem to be unconstrained. Motivated by this, we develop a family of distributed Fenchel dual gradient methods for solving constrained, strongly convex but not necessarily smooth multi-agent optimization problems over time-varying undirected networks. The proposed algorithms are constructed based on the application of weighted gradient methods to the Fenchel dual of the multi-agent optimization problem, and can be implemented in a fully decentralized fashion. We show that the proposed algorithms drive all the agents to both primal and dual optimality asymptotically under a minimal connectivity condition and at sublinear rates under a standard connectivity condition. Finally, the competent convergence performance of the distributed Fenchel dual gradient methods is demonstrated via simulations.
Cite
@article{arxiv.1708.07620,
title = {Fenchel Dual Gradient Methods for Distributed Convex Optimization over Time-varying Networks},
author = {Xuyang Wu and Jie Lu},
journal= {arXiv preprint arXiv:1708.07620},
year = {2018}
}