CLARSTA: A random subspace trust-region algorithm for convex-constrained derivative-free optimization
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917487413559296 |
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| author | Chen, Yiwen Hare, Warren Wiebe, Amy |
| author_facet | Chen, Yiwen Hare, Warren Wiebe, Amy |
| contents | This paper proposes a random subspace trust-region algorithm for general convex-constrained derivative-free optimization (DFO) problems. Similar to previous random subspace DFO methods, the convergence of our algorithm requires a certain accuracy of models and a certain quality of subspaces. For model accuracy, we define a new class of models that is only required to provide reasonable accuracy on the projection of the constraint set onto the subspace. We provide a new geometry measure to make these models easy to analyze, construct, and manage. For subspace quality, we use the concentration of measure on the Grassmann manifold to provide a method to sample subspaces that preserve the first-order criticality measure by a certain fraction with a certain probability lower bound. Based on all these new theoretical results, we present an almost-sure global convergence and a worst-case complexity analysis of our algorithm. Numerical experiments on problems with dimensions up to 10000 demonstrate the reliable performance of our algorithm in high dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | CLARSTA: A random subspace trust-region algorithm for convex-constrained derivative-free optimization Chen, Yiwen Hare, Warren Wiebe, Amy Optimization and Control 90C56, 65K05, 90C06 This paper proposes a random subspace trust-region algorithm for general convex-constrained derivative-free optimization (DFO) problems. Similar to previous random subspace DFO methods, the convergence of our algorithm requires a certain accuracy of models and a certain quality of subspaces. For model accuracy, we define a new class of models that is only required to provide reasonable accuracy on the projection of the constraint set onto the subspace. We provide a new geometry measure to make these models easy to analyze, construct, and manage. For subspace quality, we use the concentration of measure on the Grassmann manifold to provide a method to sample subspaces that preserve the first-order criticality measure by a certain fraction with a certain probability lower bound. Based on all these new theoretical results, we present an almost-sure global convergence and a worst-case complexity analysis of our algorithm. Numerical experiments on problems with dimensions up to 10000 demonstrate the reliable performance of our algorithm in high dimensions. |
| title | CLARSTA: A random subspace trust-region algorithm for convex-constrained derivative-free optimization |
| topic | Optimization and Control 90C56, 65K05, 90C06 |
| url | https://arxiv.org/abs/2506.20335 |