dc.contributor.author | Barton, Paul I | |
dc.contributor.author | Kannan, Rohit | |
dc.date.accessioned | 2018-07-23T18:24:57Z | |
dc.date.available | 2018-07-23T18:24:57Z | |
dc.date.issued | 2017-06 | |
dc.date.submitted | 2016-11 | |
dc.identifier.issn | 0925-5001 | |
dc.identifier.issn | 1573-2916 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/117047 | |
dc.description.abstract | The 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.sponsorship | BP (Firm) | en_US |
dc.publisher | Springer-Verlag | en_US |
dc.relation.isversionof | https://doi.org/10.1007/s10898-017-0532-y | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
dc.source | Springer US | en_US |
dc.title | Convergence-order analysis of branch-and-bound algorithms for constrained problems | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Kannan, 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.department | Massachusetts Institute of Technology. Department of Chemical Engineering | en_US |
dc.contributor.mitauthor | Barton, Paul I | |
dc.contributor.mitauthor | Kannan, Rohit | |
dc.relation.journal | Journal of Global Optimization | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2018-07-14T03:53:23Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | Springer Science+Business Media New York | |
dspace.orderedauthors | Kannan, Rohit; Barton, Paul I. | en_US |
dspace.embargo.terms | N | en |
dc.identifier.orcid | https://orcid.org/0000-0003-2895-9443 | |
dc.identifier.orcid | https://orcid.org/0000-0002-7963-7682 | |
mit.license | OPEN_ACCESS_POLICY | en_US |