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<p>In this paper, we develop an inexact symmetric proximal alternating direction method of multipliers (ISPADMM) with two convex combinations (ISPADMM-tcc) for solving two-block separable convex optimization problems with linear equality constraints. Specifically, the convex combination technique is incorporated into the proximal centers of both subproblems. We then approximately solve these two subproblems based on relative error criteria. The global convergence, and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10473_2025_424_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(O({1 \over N})\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>O</mi> <mo stretchy="false">(</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions, where <i>N</i> denotes the number of iterations. Finally, numerical experiments on solving the <i>l</i><sub>1</sub>-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.</p>

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An inexact symmetric proximal ADMM with convex combination proximal centers for separable convex programming

  • 期刊论文

  • 发表日期：

    2025年4月8日

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  • Jinbao Jian,
  • Xianke Tang,
  • Jianghua Yin,
  • Xianzhen Jiang

摘要

In this paper, we develop an inexact symmetric proximal alternating direction method of multipliers (ISPADMM) with two convex combinations (ISPADMM-tcc) for solving two-block separable convex optimization problems with linear equality constraints. Specifically, the convex combination technique is incorporated into the proximal centers of both subproblems. We then approximately solve these two subproblems based on relative error criteria. The global convergence, and \(O({1 \over N})\) O ( 1 N ) ergodic sublinear convergence rate measured by the function value residual and constraint violation are established under some mild conditions, where N denotes the number of iterations. Finally, numerical experiments on solving the l1-regularized analysis sparse recovery and the elastic net regularization regression problems illustrate the feasibility and effectiveness of the proposed method.