An Inexact Fenchel Dual Gradient Algorithm for Distributed Optimization

In this paper, we design a distributed algorithm for addressing constrained convex optimization over networks. The proposed algorithm is developed by substituting a projected gradient operation for a convex minimization step at each iteration of the Fenchel dual gradient (FDG) method derived in a prior work, so that the high computational load of FDG can be significantly alleviated. Such an algorithm can be viewed as a weighted inexact gradient method applied to the Fenchel dual problem, and therefore is referred to as Inexact Fenchel Dual Gradient (IFDG) algorithm. We provide rates of convergence to the optimal solution for IFDG when the local objective functions are strongly convex and smooth. Simulation results demonstrate that IFDG remarkably reduces the running time of FDG, yet its convergence performance is comparable to that of FDG.