A first-order augmented Lagrangian method for constrained minimax optimization
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910671445164032 |
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| author | Lu, Zhaosong Mei, Sanyou |
| author_facet | Lu, Zhaosong Mei, Sanyou |
| contents | In this paper we study a class of constrained minimax problems. In particular, we propose a first-order augmented Lagrangian method for solving them, whose subproblems turn out to be a much simpler structured minimax problem and are suitably solved by a first-order method developed in this paper. Under some suitable assumptions, an \emph{operation complexity} of $O(\varepsilon^{-4}\log\varepsilon^{-1})$, measured by its fundamental operations, is established for the first-order augmented Lagrangian method for finding an $\varepsilon$-KKT solution of the constrained minimax problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02060 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A first-order augmented Lagrangian method for constrained minimax optimization Lu, Zhaosong Mei, Sanyou Optimization and Control Machine Learning Numerical Analysis 90C26, 90C30, 90C47, 90C99, 65K05 In this paper we study a class of constrained minimax problems. In particular, we propose a first-order augmented Lagrangian method for solving them, whose subproblems turn out to be a much simpler structured minimax problem and are suitably solved by a first-order method developed in this paper. Under some suitable assumptions, an \emph{operation complexity} of $O(\varepsilon^{-4}\log\varepsilon^{-1})$, measured by its fundamental operations, is established for the first-order augmented Lagrangian method for finding an $\varepsilon$-KKT solution of the constrained minimax problems. |
| title | A first-order augmented Lagrangian method for constrained minimax optimization |
| topic | Optimization and Control Machine Learning Numerical Analysis 90C26, 90C30, 90C47, 90C99, 65K05 |
| url | https://arxiv.org/abs/2301.02060 |