Practical Regularized Quasi-Newton Methods with Inexact Function Values
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910049192902656 |
|---|---|
| author | Hamaguchi, Hiroki Marumo, Naoki Takeda, Akiko |
| author_facet | Hamaguchi, Hiroki Marumo, Naoki Takeda, Akiko |
| contents | Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their efficiency and scalability. These methods implicitly assume accurate function evaluations and thus may fail to converge in noisy settings. Developing fast and robust quasi-Newton methods for such scenarios is therefore crucial.
To address this issue, we propose a noise-tolerant regularized quasi-Newton method equipped with a relaxed Armijo-type line search, designed to remain stable under inaccurate function evaluations. By combining a regularization parameter update rule inspired by Objective-Function-Free Optimization and the AdaGrad-Norm method, we establish a global convergence rate of $\mathcal{O}(1/\varepsilon^2)$ for reaching a first-order stationary point under the assumed error model. We performed extensive experiments on the CUTEst benchmark collection with artificially noisy objective function evaluations, as well as with low-precision floating-point arithmetic (64-, 32-, and 16-bit). The results demonstrate that the proposed method is substantially more robust than several existing methods, while maintaining competitive practical convergence speed and computational cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10642 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Practical Regularized Quasi-Newton Methods with Inexact Function Values Hamaguchi, Hiroki Marumo, Naoki Takeda, Akiko Optimization and Control 90C53, 90C06, 65K05, 49M15 Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their efficiency and scalability. These methods implicitly assume accurate function evaluations and thus may fail to converge in noisy settings. Developing fast and robust quasi-Newton methods for such scenarios is therefore crucial. To address this issue, we propose a noise-tolerant regularized quasi-Newton method equipped with a relaxed Armijo-type line search, designed to remain stable under inaccurate function evaluations. By combining a regularization parameter update rule inspired by Objective-Function-Free Optimization and the AdaGrad-Norm method, we establish a global convergence rate of $\mathcal{O}(1/\varepsilon^2)$ for reaching a first-order stationary point under the assumed error model. We performed extensive experiments on the CUTEst benchmark collection with artificially noisy objective function evaluations, as well as with low-precision floating-point arithmetic (64-, 32-, and 16-bit). The results demonstrate that the proposed method is substantially more robust than several existing methods, while maintaining competitive practical convergence speed and computational cost. |
| title | Practical Regularized Quasi-Newton Methods with Inexact Function Values |
| topic | Optimization and Control 90C53, 90C06, 65K05, 49M15 |
| url | https://arxiv.org/abs/2603.10642 |