A unified framework for distributed optimization algorithms over time-varying directed graphs
Abstract
In this paper, we propose a framework under which the decentralized optimization algorithms suggested in JKJJ,MA, NO,NO2 can be treated in a unified manner. More precisely, we show that the distributed subgradient descent algorithms JKJJ, NO, the subgradient-push algorithm NO2, and the distributed algorithm with row-stochastic matrix MA can be derived by making suitable choices of consensus matrices, step-size and subgradient from the decentralized subgradient descent proposed in NO. As a result of such unified understanding, we provide a convergence proof that covers the algorithms in JKJJ,MA, NO,NO2 under a novel algebraic condition that is strictly weaker than the conventional graph-theoretic condition in NO. This unification also enables us to derive a new distributed optimization scheme.
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