Scholarlink

<p>In this paper, we consider the composite convex optimization problem with a linear equality constraint. We propose a practical inexact augmented Lagrangian (IAL) framework that employs two relative error criteria. Under the first criterion, we demonstrate convergence and establish sublinear ergodic convergence rates. By incorporating the second criterion, we achieve sublinear non-ergodic convergence rates. Furthermore, we determine the total iteration complexity of the IAL framework by slightly relaxing these criteria. Numerical experiments on both synthetic and real-world problems are conducted to illustrate the efficiency of the proposed IAL method.</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

Convergence rate of inexact augmented Lagrangian method with practical relative error criterion for composite convex programming

  • 期刊论文

  • 发表日期：

    2025年4月28日

查看全文
  • Yunfei Qu,
  • Xingju Cai,
  • Hongying Liu,
  • Deren Han

摘要

In this paper, we consider the composite convex optimization problem with a linear equality constraint. We propose a practical inexact augmented Lagrangian (IAL) framework that employs two relative error criteria. Under the first criterion, we demonstrate convergence and establish sublinear ergodic convergence rates. By incorporating the second criterion, we achieve sublinear non-ergodic convergence rates. Furthermore, we determine the total iteration complexity of the IAL framework by slightly relaxing these criteria. Numerical experiments on both synthetic and real-world problems are conducted to illustrate the efficiency of the proposed IAL method.