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<p>This paper investigates a class of constrained composite distributed optimization problems over time-varying unbalanced directed networks. The global objective function is formulated as the sum of local objectives, each consisting of a differentiable convex term and a non-smooth convex term. To solve this composite problem, an asynchronous distributed proximal point algorithm (AsyD-PPA) is proposed based on a prediction-correction framework and finite-time ratio consensus. In this algorithm, each node performs computations using local information and exchanges data with neighbors in an asynchronous manner. The algorithm is implemented under time-varying unbalanced directed networks using uncoordinated step sizes, which do not require knowledge of the network topology. Leveraging monotone operator theory, the boundedness and convergence of the generated sequence are rigorously established under given step-size conditions, guaranteeing convergence to critical points. Moreover, under the assumptions of Lipschitz continuity and metric regularity of the operators, linear convergence rates are derived. Finally, the effectiveness of AsyD-PPA is validated through two typical distributed optimization problems in machine learning and power system economic dispatch, where various performance-influencing factors are thoroughly investigated.</p>

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Convergence analysis of distributed composite optimization with nonlinear constraints under time-varying directed networks

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Run Tang,
  • Huaqing Li,
  • Dawen Xia,
  • Liang Ran,
  • Jun Li

摘要

This paper investigates a class of constrained composite distributed optimization problems over time-varying unbalanced directed networks. The global objective function is formulated as the sum of local objectives, each consisting of a differentiable convex term and a non-smooth convex term. To solve this composite problem, an asynchronous distributed proximal point algorithm (AsyD-PPA) is proposed based on a prediction-correction framework and finite-time ratio consensus. In this algorithm, each node performs computations using local information and exchanges data with neighbors in an asynchronous manner. The algorithm is implemented under time-varying unbalanced directed networks using uncoordinated step sizes, which do not require knowledge of the network topology. Leveraging monotone operator theory, the boundedness and convergence of the generated sequence are rigorously established under given step-size conditions, guaranteeing convergence to critical points. Moreover, under the assumptions of Lipschitz continuity and metric regularity of the operators, linear convergence rates are derived. Finally, the effectiveness of AsyD-PPA is validated through two typical distributed optimization problems in machine learning and power system economic dispatch, where various performance-influencing factors are thoroughly investigated.