Catalogo dei prodotti della ricerca
IRIS è la soluzione IT che facilita la raccolta e la gestione dei dati relativi alle attività e ai prodotti della ricerca. Fornisce a ricercatori, amministratori e valutatori gli strumenti per monitorare i risultati della ricerca, aumentarne la visibilità e allocare in modo efficace le risorse disponibili.
EnglishWe consider an iterative computation of negative curvature directions, in large-scale unconstrained optimization frameworks, needed for ensuring the convergence toward stationary pointswhich satisfy second-order necessary optimality conditions. We show that to the latter purpose, we can fruitfully couple the conjugate gradient (CG) method with a recently introduced approach involving the use of the numeral called Grossone. In particular, recalling that in principle the CG method is well posed onlywhen solving positive definite linear systems, our proposal exploits the use of grossone to enhance theperformance of the CG, allowing the computation of negative curvature directions in the indefinite case, too. Our overall method could be used to significantly generalize the theory in state-of-the-art literature. Moreover, it straightforwardly allows the solution of Newton’s equation in optimization frameworks, even in nonconvex problems. We remark that our iterative procedure to compute a negative curvature direction does not require the storage of any matrix, simply needing to store a couple of vectors. This definitely represents an advance with respect to current results in the literature.
Iterative Grossone-Based Computation of Negative Curvature Directions in Large-Scale Optimization / De Leone, Renato; Fasano, Giovanni; Roma, Massimo; Sergeyev, Yaroslav D.. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 186(2020), pp. 554-589.
| Titolo: | Iterative Grossone-Based Computation of Negative Curvature Directions in Large-Scale Optimization | |
| Autori: | ||
| Data di pubblicazione: | 2020 | |
| Rivista: | ||
| Citazione: | Iterative Grossone-Based Computation of Negative Curvature Directions in Large-Scale Optimization / De Leone, Renato; Fasano, Giovanni; Roma, Massimo; Sergeyev, Yaroslav D.. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 186(2020), pp. 554-589. | |
| Handle: | http://hdl.handle.net/11573/1433829 | |
| Appartiene alla tipologia: | 01a Articolo in rivista |
File allegati a questo prodotto
| File | Note | Tipologia | Licenza | |
|---|---|---|---|---|
| DeLeone_Iterative-Grossone-Based_2020.pdf | Versione editoriale (versione pubblicata con il layout dell'editore) |  | Open Access Visualizza/Apri |
http://hdl.handle.net/11573/1433829
Copyright © 2022