A first-order method for nonconvex-strongly-concave constrained minimax optimization
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909980866641920 |
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| author | Lu, Zhaosong Mei, Sanyou |
| author_facet | Lu, Zhaosong Mei, Sanyou |
| contents | In this paper we study a nonconvex-strongly-concave constrained minimax problem. Specifically, we propose a first-order augmented Lagrangian method for solving it, whose subproblems are nonconvex-strongly-concave unconstrained minimax problems and suitably solved by a first-order method developed in this paper that leverages the strong concavity structure. Under suitable assumptions, the proposed method achieves an operation complexity of $O(\varepsilon^{-3.5}\log\varepsilon^{-1})$, measured in terms of its fundamental operations, for finding an $\varepsilon$-KKT solution of the constrained minimax problem, which improves the previous best-known operation complexity by a factor of $\varepsilon^{-0.5}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22909 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A first-order method for nonconvex-strongly-concave 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 nonconvex-strongly-concave constrained minimax problem. Specifically, we propose a first-order augmented Lagrangian method for solving it, whose subproblems are nonconvex-strongly-concave unconstrained minimax problems and suitably solved by a first-order method developed in this paper that leverages the strong concavity structure. Under suitable assumptions, the proposed method achieves an operation complexity of $O(\varepsilon^{-3.5}\log\varepsilon^{-1})$, measured in terms of its fundamental operations, for finding an $\varepsilon$-KKT solution of the constrained minimax problem, which improves the previous best-known operation complexity by a factor of $\varepsilon^{-0.5}$. |
| title | A first-order method for nonconvex-strongly-concave constrained minimax optimization |
| topic | Optimization and Control Machine Learning Numerical Analysis 90C26, 90C30, 90C47, 90C99, 65K05 |
| url | https://arxiv.org/abs/2512.22909 |