Dual Averaging Push for Distributed Convex Optimization Over Time-Varying Directed Graph

Inspired by the subgradient push method developed recently by Nedić <italic>et al.</italic> we present a distributed dual averaging push algorithm for constrained nonsmooth convex optimization over time-varying directed graph. Our algorithm combines the dual averaging method with the push-sum technique and achieves an <inline-formula><tex-math notation="LaTeX">$O(1/ \sqrt{k})$</tex-math></inline-formula> convergence rate. Compared with the subgradient push algorithm, our algorithm, first, addresses the constrained problems, and, second, has a faster convergence rate, and, third, simplifies the convergence analysis. We also generalize the proposed algorithm so that input variables of subgradient oracles have guaranteed convergence.