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The p-Lagrangian relaxation for separable nonconvex MIQCQP problems

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Andrade, Tiago
dc.contributor.author Belyak, Nikita
dc.contributor.author Eberhard, Andrew
dc.contributor.author Hamacher, Silvio
dc.contributor.author Oliveira, Fabricio
dc.date.accessioned 2022-03-03T15:43:43Z
dc.date.available 2022-03-03T15:43:43Z
dc.date.issued 2022-02-22
dc.identifier.citation Andrade , T , Belyak , N , Eberhard , A , Hamacher , S & Oliveira , F 2022 , ' The p-Lagrangian relaxation for separable nonconvex MIQCQP problems ' , JOURNAL OF GLOBAL OPTIMIZATION , vol. 84 , no. 1 , pp. 43-76 . https://doi.org/10.1007/s10898-022-01138-y en
dc.identifier.issn 0925-5001
dc.identifier.issn 1573-2916
dc.identifier.other PURE UUID: df7eb3b4-8eb5-444b-b80e-ab8ae2eba6ef
dc.identifier.other PURE ITEMURL: https://research.aalto.fi/en/publications/df7eb3b4-8eb5-444b-b80e-ab8ae2eba6ef
dc.identifier.other PURE LINK: https://doi.org/10.1007/s10898-022-01138-y
dc.identifier.other PURE LINK: http://www.scopus.com/inward/record.url?scp=85124898043&partnerID=8YFLogxK
dc.identifier.other PURE FILEURL: https://research.aalto.fi/files/80021287/The_p_Lagrangian_relaxation_for_separable_nonconvex_MIQCQP_problems.pdf
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/113217
dc.description.abstract This paper presents a novel technique to compute Lagrangian bounds for nonconvex mixed-integer quadratically constrained quadratic programming problems presenting a separable structure (i.e., a separable problems) such as those arising in deterministic equivalent representations of two-stage stochastic programming problems. In general, the nonconvex nature of these models still poses a challenge to the available solvers, which do not consistently perform well for larger-scale instances. Therefore, we propose an appealing alternative algorithm that allows for overcoming computational performance issues. Our novel technique, named the p-Lagrangian decomposition, is a decomposition method that combines Lagrangian decomposition with mixed-integer programming-based relaxations. These relaxations are obtained using the reformulated normalised multiparametric disaggregation technique and can be made arbitrarily precise by means of a precision parameter p. We provide a technical analysis showing the convergent behaviour of the approach as the approximation is made increasingly precise. We observe that the proposed method presents significant reductions in computational time when compared with a previously proposed techniques in the literature and the direct employment of a commercial solver. Moreover, our computational experiments show that the employment of a simple heuristic can recover solutions with small duality gaps. en
dc.format.extent 34
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Springer Netherlands
dc.relation.ispartofseries JOURNAL OF GLOBAL OPTIMIZATION en
dc.rights openAccess en
dc.title The p-Lagrangian relaxation for separable nonconvex MIQCQP problems en
dc.type A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä fi
dc.description.version Peer reviewed en
dc.contributor.department PSR Energy Consulting and Analytics
dc.contributor.department Department of Mathematics and Systems Analysis
dc.contributor.department RMIT University
dc.contributor.department Pontifical Catholic University of Rio De Janeiro
dc.identifier.urn URN:NBN:fi:aalto-202203032100
dc.identifier.doi 10.1007/s10898-022-01138-y
dc.type.version publishedVersion

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