On global optimization with indefinite quadratics

We present an algorithmic framework for global optimization problems in which the non-convexity is manifested as an indefinite-quadratic as part of the objective function. Our solution approach consists of applying a spatial branch-and-bound algorithm, exploiting convexity as much as possible, not o...

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Autores principales:	Marcia Fampa, Jon Lee, Wendel Melo
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2017
Materias:	90-XX 90Cxx 90C26 90C11 90C20 90C22 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/32e24a8df238414eb7b2fde88fb79020
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spelling	oai:doaj.org-article:32e24a8df238414eb7b2fde88fb790202021-12-02T05:01:01ZOn global optimization with indefinite quadratics2192-440610.1007/s13675-016-0079-6https://doaj.org/article/32e24a8df238414eb7b2fde88fb790202017-09-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621000836https://doaj.org/toc/2192-4406We present an algorithmic framework for global optimization problems in which the non-convexity is manifested as an indefinite-quadratic as part of the objective function. Our solution approach consists of applying a spatial branch-and-bound algorithm, exploiting convexity as much as possible, not only convexity in the constraints, but also extracted from the indefinite-quadratic. A preprocessing stage is proposed to split the indefinite-quadratic into a difference of convex quadratic functions, leading to a more efficient spatial branch-and-bound focused on the isolated non-convexity. We investigate several natural possibilities for splitting an indefinite quadratic at the preprocessing stage, and prove the equivalence of some of them. Through computational experiments with our new solver iquad, we analyze how the splitting strategies affect the performance of our algorithm, and find guidelines for choosing amongst them.Marcia FampaJon LeeWendel MeloElsevierarticle90-XX90Cxx90C2690C1190C2090C22Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 5, Iss 3, Pp 309-337 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	90-XX 90Cxx 90C26 90C11 90C20 90C22 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90-XX 90Cxx 90C26 90C11 90C20 90C22 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Marcia Fampa Jon Lee Wendel Melo On global optimization with indefinite quadratics
description	We present an algorithmic framework for global optimization problems in which the non-convexity is manifested as an indefinite-quadratic as part of the objective function. Our solution approach consists of applying a spatial branch-and-bound algorithm, exploiting convexity as much as possible, not only convexity in the constraints, but also extracted from the indefinite-quadratic. A preprocessing stage is proposed to split the indefinite-quadratic into a difference of convex quadratic functions, leading to a more efficient spatial branch-and-bound focused on the isolated non-convexity. We investigate several natural possibilities for splitting an indefinite quadratic at the preprocessing stage, and prove the equivalence of some of them. Through computational experiments with our new solver iquad, we analyze how the splitting strategies affect the performance of our algorithm, and find guidelines for choosing amongst them.
format	article
author	Marcia Fampa Jon Lee Wendel Melo
author_facet	Marcia Fampa Jon Lee Wendel Melo
author_sort	Marcia Fampa
title	On global optimization with indefinite quadratics
title_short	On global optimization with indefinite quadratics
title_full	On global optimization with indefinite quadratics
title_fullStr	On global optimization with indefinite quadratics
title_full_unstemmed	On global optimization with indefinite quadratics
title_sort	on global optimization with indefinite quadratics
publisher	Elsevier
publishDate	2017
url	https://doaj.org/article/32e24a8df238414eb7b2fde88fb79020
work_keys_str_mv	AT marciafampa onglobaloptimizationwithindefinitequadratics AT jonlee onglobaloptimizationwithindefinitequadratics AT wendelmelo onglobaloptimizationwithindefinitequadratics
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On global optimization with indefinite quadratics

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