D-ripALM: A Tuning-friendly Decentralized Relative-Type Inexact Proximal Augmented Lagrangian Method
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917254241714176 |
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| author | Zhu, Jiayi Wang, Hong Liang, Ling Yang, Lei |
| author_facet | Zhu, Jiayi Wang, Hong Liang, Ling Yang, Lei |
| contents | This paper proposes D-ripALM, a Decentralized relative-type inexact proximal Augmented Lagrangian Method for consensus convex optimization over multi-agent networks. D-ripALM adopts a double-loop distributed optimization framework that accommodates a wide range of inner solvers, enabling efficient treatment of both smooth and nonsmooth objectives. In contrast to existing double-loop distributed augmented Lagrangian methods, D-ripALM employs a relative-type error criterion to regulate the switching between inner and outer iterations, resulting in a more practical and tuning-friendly algorithmic framework with enhanced numerical robustness. Moreover, we establish rigorous convergence guarantees for D-ripALM under general convexity assumptions, without requiring smoothness or strong convexity conditions commonly imposed in the distributed optimization literature. Numerical experiments further demonstrate the tuning-friendly nature of D-ripALM and its efficiency in attaining high-precision solutions with fewer communication rounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06398 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | D-ripALM: A Tuning-friendly Decentralized Relative-Type Inexact Proximal Augmented Lagrangian Method Zhu, Jiayi Wang, Hong Liang, Ling Yang, Lei Optimization and Control This paper proposes D-ripALM, a Decentralized relative-type inexact proximal Augmented Lagrangian Method for consensus convex optimization over multi-agent networks. D-ripALM adopts a double-loop distributed optimization framework that accommodates a wide range of inner solvers, enabling efficient treatment of both smooth and nonsmooth objectives. In contrast to existing double-loop distributed augmented Lagrangian methods, D-ripALM employs a relative-type error criterion to regulate the switching between inner and outer iterations, resulting in a more practical and tuning-friendly algorithmic framework with enhanced numerical robustness. Moreover, we establish rigorous convergence guarantees for D-ripALM under general convexity assumptions, without requiring smoothness or strong convexity conditions commonly imposed in the distributed optimization literature. Numerical experiments further demonstrate the tuning-friendly nature of D-ripALM and its efficiency in attaining high-precision solutions with fewer communication rounds. |
| title | D-ripALM: A Tuning-friendly Decentralized Relative-Type Inexact Proximal Augmented Lagrangian Method |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2602.06398 |