  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.
