A hybrid stochastic alternating direction method of multipliers for nonconvex and nonsmooth composite optimization

Yuxuan Zeng, Jianchao Bai, Shengjia Wang, Zhiguo Wang and Xiaojing Shen

European Journal of Operational Research, 2026, vol. 329, issue 1, 63-78

Abstract: Nonconvex and nonsmooth composite optimization problems with linear constraints have gained significant attention in practical applications. This paper proposes a hybrid stochastic Alternating Direction Method of Multipliers (ADMM) leveraging a novel hybrid estimator to solve such problems with expectation or finite-sum objective functions. Compared to existing double-loop stochastic ADMMs, our method features simpler updates enabled by a single-loop, single-sample framework, while avoiding the need for checkpoint selection. Under mild conditions, we analyze the explicit relationships between key parameters using refined Lyapunov functions and rigorously establish the sublinear convergence. To the best of our knowledge, our work is the first single-loop stochastic ADMM for solving both expectation and finite-sum problems while matching the best-known oracle complexity bound comparable to state-of-the-art double-loop stochastic ADMMs. Numerical experiments on several different nonconvex minimization tasks demonstrate the superior performance of the proposed method.

Keywords: Machine learning; Nonconvex and nonsmooth optimization; Stochastic ADMM; Hybrid stochastic estimator; Convergence complexity (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:329:y:2026:i:1:p:63-78

DOI: 10.1016/j.ejor.2025.10.024

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