dc.contributor.author | Grimstad, Bjarne Andre | |
dc.contributor.author | Knudsen, Brage Rugstad | |
dc.date.accessioned | 2020-04-28T18:23:32Z | |
dc.date.available | 2020-04-28T18:23:32Z | |
dc.date.created | 2020-04-28T15:21:33Z | |
dc.date.issued | 2020 | |
dc.identifier.issn | 0925-5001 | |
dc.identifier.uri | https://hdl.handle.net/11250/2652832 | |
dc.description.abstract | This paper studies mathematical programming formulations for solving optimization problems with piecewise polynomial (PWP) constraints. We elaborate on suitable polynomial bases as a means of efficiently representing PWPs in mathematical programs, comparing and drawing connections between the monomial basis, the Bernstein basis, and B-splines. The theory is presented for both continuous and semi-continuous PWPs. Using a disjunctive formulation, we then exploit the characteristic of common polynomial basis functions to significantly reduce the number of nonlinearities, and to suggest a bound-tightening technique for PWP constraints. We derive several extensions using Bernstein cuts, an expanded Bernstein basis, and an expanded monomial basis, which upon a standard big-M reformulation yield a set of new MINLP models. The formulations are compared by globally solving six test sets of MINLPs and a realistic petroleum production optimization problem. The proposed framework shows promising numerical performance and facilitates the solution of PWP-constrained optimization problems using standard MINLP software. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Springer | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Mathematical programming formulations for piecewise polynomial functions | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.source.journal | Journal of Global Optimization | en_US |
dc.identifier.doi | 10.1007/s10898-020-00881-4 | |
dc.identifier.cristin | 1808494 | |
dc.description.localcode | This article is licensed under a Creative Commons Attribution 4.0 International License | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |