Uncontrolled inexact information within bundle methods

We consider convex non-smooth optimization problems where additional information with uncontrolled accuracy is readily available. It is often the case when the objective function is itself the output of an optimization solver, as for large-scale energy optimization problems tackled by decomposition....

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Autores principales:	Jérôme Malick, Welington de Oliveira, Sofia Zaourar
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2017
Materias:	65K05 49J52 49M27 90C15 90C25 90C27 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/b0e12dcf7e334e8aba7a637742b02bad
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spelling	oai:doaj.org-article:b0e12dcf7e334e8aba7a637742b02bad2021-12-02T05:00:58ZUncontrolled inexact information within bundle methods2192-440610.1007/s13675-015-0060-9https://doaj.org/article/b0e12dcf7e334e8aba7a637742b02bad2017-03-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621000733https://doaj.org/toc/2192-4406We consider convex non-smooth optimization problems where additional information with uncontrolled accuracy is readily available. It is often the case when the objective function is itself the output of an optimization solver, as for large-scale energy optimization problems tackled by decomposition. In this paper, we study how to incorporate the uncontrolled linearizations into (proximal and level) bundle algorithms in view of generating better iterates and possibly accelerating the methods. We provide the convergence analysis of the algorithms using uncontrolled linearizations, and we present numerical illustrations showing they indeed speed up resolution of two stochastic optimization problems coming from energy optimization (two-stage linear problems and chance-constrained problems in reservoir management).Jérôme MalickWelington de OliveiraSofia ZaourarElsevierarticle65K0549J5249M2790C1590C2590C27Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 5, Iss 1, Pp 5-29 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	65K05 49J52 49M27 90C15 90C25 90C27 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	65K05 49J52 49M27 90C15 90C25 90C27 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Jérôme Malick Welington de Oliveira Sofia Zaourar Uncontrolled inexact information within bundle methods
description	We consider convex non-smooth optimization problems where additional information with uncontrolled accuracy is readily available. It is often the case when the objective function is itself the output of an optimization solver, as for large-scale energy optimization problems tackled by decomposition. In this paper, we study how to incorporate the uncontrolled linearizations into (proximal and level) bundle algorithms in view of generating better iterates and possibly accelerating the methods. We provide the convergence analysis of the algorithms using uncontrolled linearizations, and we present numerical illustrations showing they indeed speed up resolution of two stochastic optimization problems coming from energy optimization (two-stage linear problems and chance-constrained problems in reservoir management).
format	article
author	Jérôme Malick Welington de Oliveira Sofia Zaourar
author_facet	Jérôme Malick Welington de Oliveira Sofia Zaourar
author_sort	Jérôme Malick
title	Uncontrolled inexact information within bundle methods
title_short	Uncontrolled inexact information within bundle methods
title_full	Uncontrolled inexact information within bundle methods
title_fullStr	Uncontrolled inexact information within bundle methods
title_full_unstemmed	Uncontrolled inexact information within bundle methods
title_sort	uncontrolled inexact information within bundle methods
publisher	Elsevier
publishDate	2017
url	https://doaj.org/article/b0e12dcf7e334e8aba7a637742b02bad
work_keys_str_mv	AT jeromemalick uncontrolledinexactinformationwithinbundlemethods AT welingtondeoliveira uncontrolledinexactinformationwithinbundlemethods AT sofiazaourar uncontrolledinexactinformationwithinbundlemethods
_version_	1718400848478863360

Uncontrolled inexact information within bundle methods

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