Optimization over time-varying directed graphs with row and column-stochastic matrices
In this paper, we provide a distributed optimization algorithm, termed as TV-$\mathcal{AB}$, that minimizes a sum of convex functions over time-varying, random directed graphs. Contrary to the existing work, the algorithm we propose does not require eigenvector estimation to estimate the (non-$\math...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
17.10.2018
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Subjects | |
Online Access | Get full text |
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Summary: | In this paper, we provide a distributed optimization algorithm, termed as
TV-$\mathcal{AB}$, that minimizes a sum of convex functions over time-varying,
random directed graphs. Contrary to the existing work, the algorithm we propose
does not require eigenvector estimation to estimate the (non-$\mathbf{1}$)
Perron eigenvector of a stochastic matrix. Instead, the proposed approach
relies on a novel information mixing approach that exploits both row- and
column-stochastic weights to achieve agreement towards the optimal solution
when the underlying graph is directed. We show that TV-$\mathcal{AB}$ converges
linearly to the optimal solution when the global objective is smooth and
strongly-convex, and the underlying time-varying graphs exhibit bounded
connectivity, i.e., a union of every $C$ consecutive graphs is
strongly-connected. We derive the convergence results based on the stability
analysis of a linear system of inequalities along with a matrix perturbation
argument. Simulations confirm the findings in this paper. |
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DOI: | 10.48550/arxiv.1810.07393 |