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<p>The alternating direction method of multipliers (ADMM) has been widely applied in the field of data science. In this paper, we develop an ADMM-type scheme for solving separable convex problems with linear constraints in stochastic and large-scale models. To achieve a balance in computational load, we suggest a proximal linearization of the primal subproblem by the stochastic first-order oracle, while reshaping the dual subproblem for easier solvability. Inheriting the benefits of the balance methodology and first-order approximation, the proposed algorithm is applicable to a broad class of problems even with functions that have no closed-form solution to the subproblem. Convergence analyses are established for various cases of the objective function and a proper extrapolation has been also discussed with underlying weight. Numerical experiments demonstrate that our algorithm is effective and promising for solving problems with application to data science.</p>

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A Linearized Proximal ADMM for Stochastic and Large-scale Convex Optimization

  • 期刊论文

  • 发表日期：

    2025年7月22日

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  • Haiming Song,
  • Hao Wang,
  • Jiageng Wu,
  • Jinda Yang

摘要

The alternating direction method of multipliers (ADMM) has been widely applied in the field of data science. In this paper, we develop an ADMM-type scheme for solving separable convex problems with linear constraints in stochastic and large-scale models. To achieve a balance in computational load, we suggest a proximal linearization of the primal subproblem by the stochastic first-order oracle, while reshaping the dual subproblem for easier solvability. Inheriting the benefits of the balance methodology and first-order approximation, the proposed algorithm is applicable to a broad class of problems even with functions that have no closed-form solution to the subproblem. Convergence analyses are established for various cases of the objective function and a proper extrapolation has been also discussed with underlying weight. Numerical experiments demonstrate that our algorithm is effective and promising for solving problems with application to data science.