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In the large collection of existing distributed algorithms for convexmulti-agent optimization, only a handful of them provide convergence rateguarantees on agent networks with time-varying topologies, which, however,restrict the problem to be unconstrained. Motivated by this, we develop afamily of distributed Fenchel dual gradient methods for solving constrained,strongly convex but not necessarily smooth multi-agent optimization problemsover time-varying undirected networks. The proposed algorithms are constructedbased on the application of weighted gradient methods to the Fenchel dual ofthe multi-agent optimization problem, and can be implemented in a fullydecentralized fashion. We show that the proposed algorithms drive all theagents to both primal and dual optimality asymptotically under a minimalconnectivity condition and at sublinear rates under a standard connectivitycondition. Finally, the competent convergence performance of the distributedFenchel dual gradient methods is demonstrated via simulations.

Fenchel Dual Gradient Methods for Distributed Convex Optimization over Time-varying Networks