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Proximal nested primal-dual gradient algorithms for distributed constraint-coupled composite optimization

Published: 01 May 2023 Publication History

Highlights

The proposed Prox-NPGA can handle the non-smooth term in the objective function.
The convergences of CTA-Prox-NPGA and ATC-Prox-NPGA are proved.
The upper bounds of the step-sizes are given.
Prox-NPGA is not only an algorithm, but also an algorithmic framework.

Abstract

In this paper, we study a class of distributed constraint-coupled optimization problems, where each local function is composed of a smooth and strongly convex function and a convex but possibly non-smooth function. We design a novel proximal nested primal-dual gradient algorithm (Prox-NPGA), which is a generalized version of the exiting algorithm–NPGA. The convergence of Prox-NPGA is proved and the upper bounds of the step-sizes are given. Finally, numerical experiments are employed to verify the theoretical results and compare the convergence rates of different versions of Prox-NPGA.

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      Information & Contributors

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      Published In

      cover image Applied Mathematics and Computation
      Applied Mathematics and Computation  Volume 444, Issue C
      May 2023
      346 pages

      Publisher

      Elsevier Science Inc.

      United States

      Publication History

      Published: 01 May 2023

      Author Tags

      1. Constraint-coupled optimization
      2. Non-smooth function
      3. Proximal operator
      4. Primal-dual gradient algorithm

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