Research output per year
Research output per year
Stefania Bellavia, Gianmarco Gurioli, Benedetta Morini, Philippe L. Toint
Research output: Contribution in Book/Catalog/Report/Conference proceeding › Conference contribution
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [1]: it employs random models with accuracy guaranteed with a sufficiently large prefixed probability and deterministic inexact function evaluations within a prescribed level of accuracy. Without assuming unbiased estimators, the expected number of iterations is O( _1^ - 2 ) or O( _1^ - 3/2 ) when searching for a first-order critical point using a second or third order model, respectively, and of O( max [ _1^ - 3/2, _2^ - 3 ] ) when seeking for second-order critical points with a third order model, in which _j,j 1,2, is the j th-order tolerance. These results match the worst-case optimal complexity for the deterministic counterpart of the method. Preliminary numerical tests for first-order optimality in the context of nonconvex binary classification in imaging, with and without Artifical Neural Networks (ANNs), are presented and discussed.
Original language | English |
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Title of host publication | Proceedings - 2021 21st International Conference on Computational Science and Its Applications, ICCSA 2021 |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 258-267 |
Number of pages | 10 |
ISBN (Electronic) | 9781665458436 |
DOIs | |
Publication status | Published - 2021 |
Event | 21st International Conference on Computational Science and Its Applications, ICCSA 2021 - Cagliari, Italy Duration: 13 Sept 2021 → 16 Sept 2021 |
Name | Proceedings - 2021 21st International Conference on Computational Science and Its Applications, ICCSA 2021 |
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Conference | 21st International Conference on Computational Science and Its Applications, ICCSA 2021 |
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Country/Territory | Italy |
City | Cagliari |
Period | 13/09/21 → 16/09/21 |
Research output: Contribution to journal › Article › peer-review