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Distributed accelerated optimization algorithms: Insights from an ODE

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Abstract

In this paper, we consider the distributed optimization problem, where the goal is to minimize the global objective function formed by a sum of agents’ local smooth and strongly convex objective functions, over undirected connected graphs. Several distributed accelerated algorithms have been proposed for solving such a problem in the existing literature. In this paper, we provide insights for understanding these existing distributed algorithms from an ordinary differential equation (ODE) point of view. More specifically, we first derive an equivalent second-order ODE, which is the exact limit of these existing algorithms by taking the small step-size. Moreover, focusing on the quadratic objective functions, we show that the solution of the resulting ODE exponentially converges to the unique global optimal solution. The theoretical results are validated and illustrated by numerical simulations.

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Authors and Affiliations

  1. School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    RuiJuan Chen

  2. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, China

    Tao Yang & TianYou Chai

Authors
  1. RuiJuan Chen
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  2. Tao Yang
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  3. TianYou Chai
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Corresponding author

Correspondence to Tao Yang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 91748112, 61991403, 61991404, and 61991400).

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Chen, R., Yang, T. & Chai, T. Distributed accelerated optimization algorithms: Insights from an ODE. Sci. China Technol. Sci. 63, 1647–1655 (2020). https://doi.org/10.1007/s11431-020-1596-8

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  • DOI: https://doi.org/10.1007/s11431-020-1596-8

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