Q-Linear Convergence of the Proximal Augmented Lagrangian Method for Non-Convex Conic Programming
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915494350553088 |
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| author | Zhang, Ning Zhang, Yi |
| author_facet | Zhang, Ning Zhang, Yi |
| contents | This paper provides a local convergence analysis of the proximal augmented Lagrangian method (PALM) applied to a class of non-convex conic programming problems. Previous convergence results for PALM typically imposed assumptions such as constraint non-degeneracy, strict complementarity, second-order sufficiency conditions, or a combination of constraint nondegeneracy with strong second-order sufficiency conditions. In contrast, our work demonstrates a Q-linear convergence rate for an inexact version of PALM in the context of non-convex conic programming, without requiring the uniqueness of the Lagrange multipliers. The analysis relies solely on the second-order sufficiency condition and the calmness property of the multiplier mapping, presenting a more relaxed set of conditions for ensuring convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Q-Linear Convergence of the Proximal Augmented Lagrangian Method for Non-Convex Conic Programming Zhang, Ning Zhang, Yi Optimization and Control 9C30 This paper provides a local convergence analysis of the proximal augmented Lagrangian method (PALM) applied to a class of non-convex conic programming problems. Previous convergence results for PALM typically imposed assumptions such as constraint non-degeneracy, strict complementarity, second-order sufficiency conditions, or a combination of constraint nondegeneracy with strong second-order sufficiency conditions. In contrast, our work demonstrates a Q-linear convergence rate for an inexact version of PALM in the context of non-convex conic programming, without requiring the uniqueness of the Lagrange multipliers. The analysis relies solely on the second-order sufficiency condition and the calmness property of the multiplier mapping, presenting a more relaxed set of conditions for ensuring convergence. |
| title | Q-Linear Convergence of the Proximal Augmented Lagrangian Method for Non-Convex Conic Programming |
| topic | Optimization and Control 9C30 |
| url | https://arxiv.org/abs/2509.11531 |