Nonsmooth spectral gradient methods for unconstrained optimization
| dc.contributor.author | Loreto, Milagros C. | |
| dc.contributor.author | Aponte, Hugo | |
| dc.contributor.author | Cores, Débora | |
| dc.contributor.author | Raydan, Marcos | |
| dc.date.accessioned | 2025-01-28T08:57:36Z | |
| dc.date.available | 2025-01-28T08:57:36Z | |
| dc.date.issued | 2017 | |
| dc.description.abstract | To solve nonsmooth unconstrained minimization problems, we combine the spectral choice of step length with two well-established subdifferential-type schemes: the gradient sampling method and the simplex gradient method. We focus on the interesting case in which the objective function is continuously differentiable almost everywhere, and it is of- ten not differentiable at minimizers. In the case of the gradient sampling method, we also present a simple differentiability test that allows us to use the exact gradient direction as frequently as possible, and to build a stochastic subdifferential direction only if the test fails. The proposed spectral gradient sampling method is combined with a monotone line search globalization strategy. On the other hand, the simplex gradient method is a direct search method that only requires function evaluations to build an approximation to the gradient direction. In this case, the proposed spectral simplex gradient method is combined with a suitable nonmonotone line search strategy. For both scenarios, we present preliminary nu- merical results on a set of nonsmooth test functions. These numerical results indicate that using a spectral step length can improve the practical performance of both methods. | |
| dc.identifier.citation | Euro Journal on Computational Optimization, 5(4), 529-553, 2017 | |
| dc.identifier.issn | 2192-4414 | |
| dc.identifier.uri | http://calderon.cud.uvigo.es/handle/123456789/882 | |
| dc.language.iso | en | |
| dc.publisher | Euro Journal on Computational Optimization | |
| dc.title | Nonsmooth spectral gradient methods for unconstrained optimization | |
| dc.type | Article |