Faster Stochastic ADMM for Nonsmooth Composite Convex Optimization in Hilbert Space
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913131630952448 |
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| author | Deng, Weihua Song, Haiming Wang, Hao Yang, Jinda |
| author_facet | Deng, Weihua Song, Haiming Wang, Hao Yang, Jinda |
| contents | In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by partial differential equation (PDE) with random coefficients. We prove the strong convergence of the proposed ADMM algorithm in the strongly convex case, and show the faster nonergodic convergence rates in terms of functional values and feasibility violation for both strongly convex and general convex cases. We demonstrate the application of the proposed method to solve certain model problems, along with its associated probability bound of large deviation. Some preliminary numerical results illustrate the efficiency of our method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09447 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Faster Stochastic ADMM for Nonsmooth Composite Convex Optimization in Hilbert Space Deng, Weihua Song, Haiming Wang, Hao Yang, Jinda Optimization and Control In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by partial differential equation (PDE) with random coefficients. We prove the strong convergence of the proposed ADMM algorithm in the strongly convex case, and show the faster nonergodic convergence rates in terms of functional values and feasibility violation for both strongly convex and general convex cases. We demonstrate the application of the proposed method to solve certain model problems, along with its associated probability bound of large deviation. Some preliminary numerical results illustrate the efficiency of our method. |
| title | Faster Stochastic ADMM for Nonsmooth Composite Convex Optimization in Hilbert Space |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2603.09447 |