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In this paper, we provide a distributed optimization algorithm, termed asTV-$\mathcal{AB}$, that minimizes a sum of convex functions over time-varying,random directed graphs. Contrary to the existing work, the algorithm we proposedoes not require eigenvector estimation to estimate the (non-$\mathbf{1}$)Perron eigenvector of a stochastic matrix. Instead, the proposed approachrelies on a novel information mixing approach that exploits both row- andcolumn-stochastic weights to achieve agreement towards the optimal solutionwhen the underlying graph is directed. We show that TV-$\mathcal{AB}$ convergeslinearly to the optimal solution when the global objective is smooth andstrongly-convex, and the underlying time-varying graphs exhibit boundedconnectivity, i.e., a union of every $C$ consecutive graphs isstrongly-connected. We derive the convergence results based on the stabilityanalysis of a linear system of inequalities along with a matrix perturbationargument. Simulations confirm the findings in this paper.

Optimization over time-varying directed graphs with row and column-stochastic matrices