Fenchel Dual Gradient Methods for Distributed Convex Optimization Over Time-Varying Networks

Abstract

To date, a large collection of distributed algorithms for convex multi-agent optimization have been reported, yet only few of them converge to an optimal solution at guaranteed rates when the topologies of the agent networks are time-varying. Motivated by this, we develop a family of distributed Fenchel dual gradient methods for solving strongly convex yet non-smooth multi-agent optimization problems with nonidentical local constraints over time-varying networks. The proposed algorithms are constructed based on the application of weighted gradient methods to the Fenchel dual of the multiagent optimization problem. They are able to drive all the agents to dual optimality at an O(1/k) rate and to primal optimality at an O(1/√k) rate under a standard network connectivity condition. The competent convergence performance of the Fenchel dual gradient methods is demonstrated via numerical examples.