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Convergence of one-step projected gradient methods for variational inequalities / Paul-Emile Maingé in Journal of Optimization Theory and Applications, vol 171 n° 1 (October 2016)  

Public [article]  inJournal of Optimization Theory and Applications > vol 171 n° 1 (October 2016) . - pp 146 - 168 Titre : Convergence of one-step projected gradient methods for variational inequalities Type de document : Article/Communication Auteurs : Paul-Emile Maingé, Auteur ; Marie-Line Gobinddass , Auteur Année de publication : 2016 Article en page(s) : pp 146 - 168 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique [Termes IGN] algorithme du gradient [Termes IGN] calcul variationnel [Termes IGN] optimisation (mathématiques) Résumé : (auteur) In this paper, we revisit the numerical approach to some classical variational inequalities, with monotone and Lipschitz continuous mapping A, by means of a projected reflected gradient-type method. A main feature of the method is that it formally requires only one projection step onto the feasible set and one evaluation of the involved mapping per iteration. Contrary to what was done so far, we establish the convergence of the method in a more general setting that allows us to use varying step-sizes without any requirement of additional projections. A linear convergence rate is obtained, when A is assumed to be strongly monotone. Preliminary numerical experiments are also performed. Numéro de notice : A2016-973 Affiliation des auteurs : LASTIG LAREG+Ext (2012-mi2018) Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s10957-016-0972-4 Date de publication en ligne : 06/07/2016 En ligne : http://dx.doi.org/10.1007/s10957-016-0972-4 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=94217 [article]