An Inexact Weighted Proximal Trust-Region Method
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| Format: | Preprint |
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2026
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| _version_ | 1866915727865282560 |
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| author | Maia, Leandro Farias Baraldi, Robert Kouri, Drew P. |
| author_facet | Maia, Leandro Farias Baraldi, Robert Kouri, Drew P. |
| contents | In [R. J. Baraldi and D. P. Kouri, Math. Program., 201:1 (2023), pp. 559-598], the authors introduced a trust-region method for minimizing the sum of a smooth nonconvex and a nonsmooth convex function, the latter of which has an analytical proximity operator. While many functions satisfy this criterion, e.g., the $\ell_1$-norm defined on $\ell_2$, many others are precluded by either the topology or the nature of the nonsmooth term. Using the $δ$-Fréchet subdifferential, we extend the definition of the inexact proximity operator and enable its use within the aforementioned trust-region algorithm. Moreover, we augment the analysis for the standard trust-region convergence theory to handle proximity operator inexactness with weighted inner products. We first introduce an algorithm to generate a point in the inexact proximity operator and then apply the algorithm within the trust-region method to solve an optimal control problem constrained by Burgers' equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_09024 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Inexact Weighted Proximal Trust-Region Method Maia, Leandro Farias Baraldi, Robert Kouri, Drew P. Optimization and Control Machine Learning In [R. J. Baraldi and D. P. Kouri, Math. Program., 201:1 (2023), pp. 559-598], the authors introduced a trust-region method for minimizing the sum of a smooth nonconvex and a nonsmooth convex function, the latter of which has an analytical proximity operator. While many functions satisfy this criterion, e.g., the $\ell_1$-norm defined on $\ell_2$, many others are precluded by either the topology or the nature of the nonsmooth term. Using the $δ$-Fréchet subdifferential, we extend the definition of the inexact proximity operator and enable its use within the aforementioned trust-region algorithm. Moreover, we augment the analysis for the standard trust-region convergence theory to handle proximity operator inexactness with weighted inner products. We first introduce an algorithm to generate a point in the inexact proximity operator and then apply the algorithm within the trust-region method to solve an optimal control problem constrained by Burgers' equation. |
| title | An Inexact Weighted Proximal Trust-Region Method |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2601.09024 |