Global optimization of multivariable functions satisfying the Vanderbei condition
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866910335420596224 |
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| author | Arutyunova, Natalya Dulliev, Aidar Zabotin, Vladislav |
| author_facet | Arutyunova, Natalya Dulliev, Aidar Zabotin, Vladislav |
| contents | We propose two algorithms for solving global optimization problems on a hyperrectangle with an objective function satisfying the Vanderbei condition (this function is also called an $\varepsilon$-Lipschitz continuous function). The algorithms belong to the class of non-uniform cover-ings methods. For the algorithms we prove propositions about convergence to an $\varepsilon$-solution in terms of the objective function. We illustrate the performance of the algorithms using several test numerical examples with non-Lipschitz continuous objective functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1912_13016 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Global optimization of multivariable functions satisfying the Vanderbei condition Arutyunova, Natalya Dulliev, Aidar Zabotin, Vladislav Optimization and Control Primary, 90C26, Secondary, 90C56, 90C57, 65K05 We propose two algorithms for solving global optimization problems on a hyperrectangle with an objective function satisfying the Vanderbei condition (this function is also called an $\varepsilon$-Lipschitz continuous function). The algorithms belong to the class of non-uniform cover-ings methods. For the algorithms we prove propositions about convergence to an $\varepsilon$-solution in terms of the objective function. We illustrate the performance of the algorithms using several test numerical examples with non-Lipschitz continuous objective functions. |
| title | Global optimization of multivariable functions satisfying the Vanderbei condition |
| topic | Optimization and Control Primary, 90C26, Secondary, 90C56, 90C57, 65K05 |
| url | https://arxiv.org/abs/1912.13016 |