The role of the steplength selection strategies in gradient methods has been widely in- vestigated in the last decades. Starting from the work of Barzilai and Borwein (1988), many efficient steplength rules have been designed, that contributed to make the gradient approaches an effective tool for the large-scale optimization problems arising in important real-world applications. Most of these steplength rules have been thought in unconstrained optimization, with the aim of exploiting some second-order information for achieving a fast annihilation of the gradient of the objective function. However, these rules are successfully used also within gradient projection methods for constrained optimization, though, to our knowledge, a detailed analysis of the effects of the constraints on the steplength selections is still not available. In this work we investigate how the presence of the box constraints affects the spectral properties of the Barzilai–Borwein rules in quadratic programming problems. The proposed analysis suggests the introduction of new steplength selection strategies specifically designed for taking account of the active constraints at each iteration. The results of a set of numerical experiments show the effectiveness of the new rules with respect to other state of the art steplength selections and their potential usefulness also in case of box-constrained non-quadratic optimization problems.
Steplength selection in gradient projection methods for box-constrained quadratic programs / Crisci, Serena; Ruggiero, Valeria; Zanni, Luca. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - 356(2019), pp. 312-327.
|Data di pubblicazione:||2019|
|Titolo:||Steplength selection in gradient projection methods for box-constrained quadratic programs|
|Autore/i:||Crisci, Serena; Ruggiero, Valeria; Zanni, Luca|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/j.amc.2019.03.039|
|Codice identificativo ISI:||WOS:000464931100022|
|Codice identificativo Scopus:||2-s2.0-85063648311|
|Citazione:||Steplength selection in gradient projection methods for box-constrained quadratic programs / Crisci, Serena; Ruggiero, Valeria; Zanni, Luca. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - 356(2019), pp. 312-327.|
|Tipologia||Articolo su rivista|
I documenti presenti in Iris Unimore sono rilasciati con licenza Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia, salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris