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<p>In this work, we first introduce a two-step inertial proximal Bregman ADMM with dual relaxation approach for solving a group of nonsmooth three-block linear constrained optimization problems in the absence of convexity. The introduced algorithm incorporates two-step inertial effect to each subproblem and integrates two relaxed terms to dual update. A straightforward sufficient condition is employed to demonstrate the boundedness of the sequence generated by the algorithm, and the global convergence is proved in light of Kurdyka-Łojasiewicz property. Furthermore, we extend the algorithm to multi-step inertial version to tackle multi-block problems. Finally, numerical experiments showcase the advantages and efficiency of the proposed algorithms.</p>

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Inertial proximal Bregman ADMM with dual relaxation approach for nonconvex optimization

  • 期刊论文

  • 发表日期：

    2025年6月20日

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  • Yazheng Dang,
  • Kaiyuan Yang,
  • Can Yang

摘要

In this work, we first introduce a two-step inertial proximal Bregman ADMM with dual relaxation approach for solving a group of nonsmooth three-block linear constrained optimization problems in the absence of convexity. The introduced algorithm incorporates two-step inertial effect to each subproblem and integrates two relaxed terms to dual update. A straightforward sufficient condition is employed to demonstrate the boundedness of the sequence generated by the algorithm, and the global convergence is proved in light of Kurdyka-Łojasiewicz property. Furthermore, we extend the algorithm to multi-step inertial version to tackle multi-block problems. Finally, numerical experiments showcase the advantages and efficiency of the proposed algorithms.