Inexact Restoration via random models for unconstrained noisy optimization
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911460040376320 |
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| author | Morini, Benedetta Rebegoldi, Simone |
| author_facet | Morini, Benedetta Rebegoldi, Simone |
| contents | We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when the evaluation of both the function and its gradient is random and a specified accuracy of such evaluations is guaranteed with sufficiently high probability. The proposed algorithm combines the Inexact Restoration framework with a trust-region methodology based on random first-order models. We analyse the properties of the algorithm and provide the expected number of iterations performed to reach an approximate first-order optimality point. Numerical experiments show that the proposed algorithm compares well with a state-of-the-art competitor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inexact Restoration via random models for unconstrained noisy optimization Morini, Benedetta Rebegoldi, Simone Optimization and Control 65K05, 90C30, 90C15 We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when the evaluation of both the function and its gradient is random and a specified accuracy of such evaluations is guaranteed with sufficiently high probability. The proposed algorithm combines the Inexact Restoration framework with a trust-region methodology based on random first-order models. We analyse the properties of the algorithm and provide the expected number of iterations performed to reach an approximate first-order optimality point. Numerical experiments show that the proposed algorithm compares well with a state-of-the-art competitor. |
| title | Inexact Restoration via random models for unconstrained noisy optimization |
| topic | Optimization and Control 65K05, 90C30, 90C15 |
| url | https://arxiv.org/abs/2402.12069 |