| Autor: |
Sahin, Mehmet Fatih, Eftekhari, Armin, Alacaoglu, Ahmet, Latorre, Fabian, Cevher, Volkan |
| Rok vydání: |
2019 |
| Předmět: |
|
| Zdroj: |
In proceedings of NeurIPS 2019, pages 13943-13955, volume 32: http://papers.nips.cc/paper/9545-an-inexact-augmented-lagrangian-framework-for-nonconvex-optimization-with-nonlinear-constraints |
| Druh dokumentu: |
Working Paper |
| Popis: |
We propose a practical inexact augmented Lagrangian method (iALM) for nonconvex problems with nonlinear constraints. We characterize the total computational complexity of our method subject to a verifiable geometric condition, which is closely related to the Polyak-Lojasiewicz and Mangasarian-Fromowitz conditions. In particular, when a first-order solver is used for the inner iterates, we prove that iALM finds a first-order stationary point with $\tilde{\mathcal{O}}(1/\epsilon^4)$ calls to the first-order oracle. If, in addition, the problem is smooth and a second-order solver is used for the inner iterates, iALM finds a second-order stationary point with $\tilde{\mathcal{O}}(1/\epsilon^5)$ calls to the second-order oracle, which matches the known theoretical complexity result in the literature. We also provide strong numerical evidence on large-scale machine learning problems, including the Burer-Monteiro factorization of semidefinite programs, and a novel nonconvex relaxation of the standard basis pursuit template. For these examples, we also show how to verify our geometric condition. |
| Databáze: |
arXiv |
| Externí odkaz: |
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