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<p>This study focuses on the distributed convex optimization problem with local boundary constraints and multiple inequality constraints, specifically considering scenarios involving communication delays and inconsistent updates between nodes. To tackle the problem with guaranteed constraint satisfaction, a distributed asynchronous optimization algorithm is proposed based on the parameter projection method. Moreover, an asynchronous gradient tracking mechanism is employed to accelerate convergence. In the convergence analysis, an augmented synchronous system with virtual nodes is adopted to transform the delayed optimization problem into a problem without delays. Based on the generalized small gain theory, the proposed algorithm is proved to achieve a geometric convergence rate. Finally, numerical simulations and industrial experiments verify the effectiveness of the proposed algorithm.</p>

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Asynchronous distributed algorithm for constrained optimization and its application

  • 期刊论文

  • 发表日期：

    2025年4月27日

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  • Ting Wang,
  • Zhongmei Li,
  • Rong Nie,
  • Wenli Du

摘要

This study focuses on the distributed convex optimization problem with local boundary constraints and multiple inequality constraints, specifically considering scenarios involving communication delays and inconsistent updates between nodes. To tackle the problem with guaranteed constraint satisfaction, a distributed asynchronous optimization algorithm is proposed based on the parameter projection method. Moreover, an asynchronous gradient tracking mechanism is employed to accelerate convergence. In the convergence analysis, an augmented synchronous system with virtual nodes is adopted to transform the delayed optimization problem into a problem without delays. Based on the generalized small gain theory, the proposed algorithm is proved to achieve a geometric convergence rate. Finally, numerical simulations and industrial experiments verify the effectiveness of the proposed algorithm.