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dc.contributor.authorBarton, Paul I
dc.contributor.authorKannan, Rohit
dc.date.accessioned2018-07-23T18:24:57Z
dc.date.available2018-07-23T18:24:57Z
dc.date.issued2017-06
dc.date.submitted2016-11
dc.identifier.issn0925-5001
dc.identifier.issn1573-2916
dc.identifier.urihttp://hdl.handle.net/1721.1/117047
dc.description.abstractThe performance of branch-and-bound algorithms for deterministic global optimization is strongly dependent on the ability to construct tight and rapidly convergent schemes of lower bounds. One metric of the efficiency of a branch-and-bound algorithm is the convergence order of its bounding scheme. This article develops a notion of convergence order for lower bounding schemes for constrained problems, and defines the convergence order of convex relaxation-based and Lagrangian dual-based lower bounding schemes. It is shown that full-space convex relaxation-based lower bounding schemes can achieve first-order convergence under mild assumptions. Furthermore, such schemes can achieve second-order convergence at KKT points, at Slater points, and at infeasible points when second-order pointwise convergent schemes of relaxations are used. Lagrangian dual-based full-space lower bounding schemes are shown to have at least as high a convergence order as convex relaxation-based full-space lower bounding schemes. Additionally, it is shown that Lagrangian dual-based full-space lower bounding schemes achieve first-order convergence even when the dual problem is not solved to optimality. The convergence order of some widely-applicable reduced-space lower bounding schemes is also analyzed, and it is shown that such schemes can achieve first-order convergence under suitable assumptions. Furthermore, such schemes can achieve second-order convergence at KKT points, at unconstrained points in the reduced-space, and at infeasible points under suitable assumptions when the problem exhibits a specific separable structure. The importance of constraint propagation techniques in boosting the convergence order of reduced-space lower bounding schemes (and helping mitigate clustering in the process) for problems which do not possess such a structure is demonstrated.en_US
dc.description.sponsorshipBP (Firm)en_US
dc.publisherSpringer-Verlagen_US
dc.relation.isversionofhttps://doi.org/10.1007/s10898-017-0532-yen_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourceSpringer USen_US
dc.titleConvergence-order analysis of branch-and-bound algorithms for constrained problemsen_US
dc.typeArticleen_US
dc.identifier.citationKannan, Rohit, and Paul I. Barton. “Convergence-Order Analysis of Branch-and-Bound Algorithms for Constrained Problems.” Journal of Global Optimization 71, no. 4 (June 1, 2017): 753–813.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Chemical Engineeringen_US
dc.contributor.mitauthorBarton, Paul I
dc.contributor.mitauthorKannan, Rohit
dc.relation.journalJournal of Global Optimizationen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2018-07-14T03:53:23Z
dc.language.rfc3066en
dc.rights.holderSpringer Science+Business Media New York
dspace.orderedauthorsKannan, Rohit; Barton, Paul I.en_US
dspace.embargo.termsNen
dc.identifier.orcidhttps://orcid.org/0000-0003-2895-9443
dc.identifier.orcidhttps://orcid.org/0000-0002-7963-7682
mit.licenseOPEN_ACCESS_POLICYen_US


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