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

Haiming Song (), Hao Wang (), Jiageng Wu () and Jinda Yang ()
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Haiming Song: Jilin University, Changchun
Hao Wang: Jilin University, Changchun
Jiageng Wu: Jilin University, Changchun
Jinda Yang: Lanzhou University, Lanzhou

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 2, No 6, 31 pages

Abstract: Abstract 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.

Keywords: Alternating direction method of multipliers; Convex optimization; Stochastic and large-scale optimization; Proximal algorithm; 62L20; 68W40; 90C15; 90C25 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02773-7

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