Convergence of trust-region algorithms in metric spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908402832113664 |
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| author | Manns, Paul |
| author_facet | Manns, Paul |
| contents | Trust-region algorithms can be applied to very abstract optimization problems because they do not require a specific direction of descent or gradient. This has lead to recent interest in them, in particular in the area of integer optimal control problems, where the infinite-dimensional problem formulations do not assume vector space structure.
We analyze a trust-region algorithm in the abstract setting of a metric space, a setting in which integer optimal control problems with total variation regularization can be formulated. Our analysis avoids a reset of the trust-region radius upon acceptance of the iterates when proving convergence to stationary points. This reset has been present in previous analyses of trust-region algorithms for integer optimal control problems. Our computational benchmark shows that the runtime can be considerably improved when avoiding this reset, which is now theoretically justified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11991 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence of trust-region algorithms in metric spaces Manns, Paul Optimization and Control 90C48 Trust-region algorithms can be applied to very abstract optimization problems because they do not require a specific direction of descent or gradient. This has lead to recent interest in them, in particular in the area of integer optimal control problems, where the infinite-dimensional problem formulations do not assume vector space structure. We analyze a trust-region algorithm in the abstract setting of a metric space, a setting in which integer optimal control problems with total variation regularization can be formulated. Our analysis avoids a reset of the trust-region radius upon acceptance of the iterates when proving convergence to stationary points. This reset has been present in previous analyses of trust-region algorithms for integer optimal control problems. Our computational benchmark shows that the runtime can be considerably improved when avoiding this reset, which is now theoretically justified. |
| title | Convergence of trust-region algorithms in metric spaces |
| topic | Optimization and Control 90C48 |
| url | https://arxiv.org/abs/2412.11991 |