Scholarlink

<p>In this paper, we focus on a class of two block nonconvex nonsmooth optimization problem with linear constraints. Firstly, we propose a Bregman-type improved alternating direction method of multiplie (ADMM) by combining the extrapolation technique. Subsequently, to reduce the difficulty of solving the subproblem, we generalize it to the linear variant by linearizing the smooth component. By assuming the merit function satisfies Kurdyka-Łojasiewicz (KŁ) property, we prove that the whole sequence generated by each proposed algorithm converges to a unique critical point of the augmented Lagrangian function (ALF). The convergence rates for the iteration sequence and the merit function value sequence are also provided. Eventually, we perform experiments on Lasso model and verify the effciency of our proposed algorithms.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Bregman-Type Improved ADMM Method with Extrapolation and Its Linear Variant for Nonconvex and Nonsmooth Optimization

  • 期刊论文

  • 发表日期：

    2025年7月17日

查看全文
  • Longhui Liu,
  • Congying Han,
  • Tiande Guo

摘要

In this paper, we focus on a class of two block nonconvex nonsmooth optimization problem with linear constraints. Firstly, we propose a Bregman-type improved alternating direction method of multiplie (ADMM) by combining the extrapolation technique. Subsequently, to reduce the difficulty of solving the subproblem, we generalize it to the linear variant by linearizing the smooth component. By assuming the merit function satisfies Kurdyka-Łojasiewicz (KŁ) property, we prove that the whole sequence generated by each proposed algorithm converges to a unique critical point of the augmented Lagrangian function (ALF). The convergence rates for the iteration sequence and the merit function value sequence are also provided. Eventually, we perform experiments on Lasso model and verify the effciency of our proposed algorithms.