{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:24:06Z","timestamp":1740122646691,"version":"3.37.3"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,3,18]],"date-time":"2024-03-18T00:00:00Z","timestamp":1710720000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,3,18]],"date-time":"2024-03-18T00:00:00Z","timestamp":1710720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"AFOSR GRANT","award":["FA9550-21-0107","FA9550-21-0107"],"award-info":[{"award-number":["FA9550-21-0107","FA9550-21-0107"]}]},{"DOI":"10.13039\/501100006463","name":"Bayerisches Staatsministerium f\u00fcr Wirtschaft und Medien, Energie und Technologie","doi-asserted-by":"publisher","award":["Center for Analytics \u2013 Data \u2013 Applications (ADA-Center) within the framework of \u201cBAYERN DIGITAL II\u201d"],"award-info":[{"award-number":["Center for Analytics \u2013 Data \u2013 Applications (ADA-Center) within the framework of \u201cBAYERN DIGITAL II\u201d"]}],"id":[{"id":"10.13039\/501100006463","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2024,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bounded and extend the well-known MIP relaxation <jats:italic>normalized multiparametric disaggregation technique<\/jats:italic>(NMDT), applying a sophisticated discretization to both variables. We refer to this approach as <jats:italic>doubly discretized normalized multiparametric disaggregation technique<\/jats:italic> (D-NMDT). In a comprehensive theoretical analysis, we underline the theoretical advantages of the enhanced method D-NMDT compared to NMDT. Furthermore, we perform a broad computational study to demonstrate its effectiveness in terms of producing tight dual bounds for MIQCQPs. Finally, we compare D-NMDT to the separable MIP relaxations from Part I and a state-of-the-art MIQCQP solver.<\/jats:p>","DOI":"10.1007\/s10589-024-00554-y","type":"journal-article","created":{"date-parts":[[2024,3,18]],"date-time":"2024-03-18T03:01:45Z","timestamp":1710730905000},"page":"893-934","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: part II"],"prefix":"10.1007","volume":"87","author":[{"given":"Benjamin","family":"Beach","sequence":"first","affiliation":[]},{"given":"Robert","family":"Burlacu","sequence":"additional","affiliation":[]},{"given":"Andreas","family":"B\u00e4rmann","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5002-2919","authenticated-orcid":false,"given":"Lukas","family":"Hager","sequence":"additional","affiliation":[]},{"given":"Robert","family":"Hildebrand","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,3,18]]},"reference":[{"issue":"2","key":"554_CR1","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1287\/ijoc.2023.1270","volume":"35","author":"K-M Aigner","year":"2023","unstructured":"Aigner, K.-M., Burlacu, R., Liers, F., Martin, A.: Solving ac optimal power flow with discrete decisions to global optimality. INFORMS J. Comput. 35(2), 458\u2013474 (2023)","journal-title":"INFORMS J. Comput."},{"key":"554_CR2","first-page":"85","volume":"1\u201331","author":"A B\u00e4rmann","year":"2022","unstructured":"B\u00e4rmann, A., Burlacu, R., Hager, L., Kleinert, T.: On piecewise linear approximations of bilinear terms: structural comparison of univariate and bivariate mixed-integer programming formulations. J. Global Optim. 1\u201331, 85 (2022)","journal-title":"J. Global Optim."},{"key":"554_CR3","unstructured":"Beach, B., Burlacu, R., B\u00e4rmann, A., Hager, L., Hildebrand, R.: Enhancements of discretization approaches for non-convex mixed-integer quadratically constraint quadratic programming: Part I. arXiv preprint arXiv:2211.00876 (2022)"},{"key":"554_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2020.106839","volume":"141","author":"B Beach","year":"2020","unstructured":"Beach, B., Hildebrand, R., Ellis, K., Lebreton, B.: An approximate method for the optimization of long-horizon tank blending and scheduling operations. Comput. Chem. Eng. 141, 106839 (2020)","journal-title":"Comput. Chem. Eng."},{"key":"554_CR5","doi-asserted-by":"crossref","unstructured":"Beach, B., Hildebrand, R., Huchette, J.: Compact mixed-integer programming formulations in quadratic optimization. J. Global Optim. (2022)","DOI":"10.1007\/s10898-022-01184-6"},{"issue":"1","key":"554_CR6","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1080\/10556788.2018.1556661","volume":"35","author":"R Burlacu","year":"2020","unstructured":"Burlacu, R., Gei\u00dfler, B., Schewe, L.: Solving mixed-integer nonlinear programmes using adaptively refined mixed-integer linear programmes. Optim. Methods Softw. 35(1), 37\u201364 (2020)","journal-title":"Optim. Methods Softw."},{"issue":"4","key":"554_CR7","doi-asserted-by":"publisher","first-page":"765","DOI":"10.1007\/s10898-015-0342-z","volume":"64","author":"PM Castro","year":"2015","unstructured":"Castro, P.M.: Normalized multiparametric disaggregation: an efficient relaxation for mixed-integer bilinear problems. J. Global Optim. 64(4), 765\u2013784 (2015)","journal-title":"J. Global Optim."},{"issue":"1","key":"554_CR8","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s12532-011-0033-9","volume":"4","author":"J Chen","year":"2012","unstructured":"Chen, J., Burer, S.: Globally solving nonconvex quadratic programming problems via completely positive programming. Math. Program. Comput. 4(1), 33\u201352 (2012)","journal-title":"Math. Program. Comput."},{"key":"554_CR9","unstructured":"Coffrin, C., Gordon, D., Scott, P.: NESTA, the NICTA energy system test case archive. arXiv preprint arXiv:1411.0359 (2014)"},{"issue":"2","key":"554_CR10","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91(2), 201\u2013213 (2002)","journal-title":"Math. Program."},{"key":"554_CR11","unstructured":"Dong, H., Luo, Y.: Compact disjunctive approximations to nonconvex quadratically constrained programs (2018)"},{"issue":"2","key":"554_CR12","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/s12532-018-0147-4","volume":"11","author":"F Furini","year":"2019","unstructured":"Furini, F., Traversi, E., Belotti, P., Frangioni, A., Gleixner, A., Gould, N., Liberti, L., Lodi, A., Misener, R., Mittelmann, H., et al.: Qplib: a library of quadratic programming instances. Math. Program. Comput. 11(2), 237\u2013265 (2019)","journal-title":"Math. Program. Comput."},{"key":"554_CR13","unstructured":"Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual (2022)"},{"key":"554_CR14","unstructured":"Huchette, J.A.: Advanced mixed-integer programming formulations: methodology, computation, and application. PhD thesis, Massachusetts Institute of Technology (2018)"},{"issue":"2","key":"554_CR15","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s10107-005-0582-7","volume":"103","author":"J Linderoth","year":"2005","unstructured":"Linderoth, J.: A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs. Math. Program. 103(2), 251\u2013282 (2005)","journal-title":"Math. Program."},{"issue":"1","key":"554_CR16","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/BF01580665","volume":"10","author":"GP McCormick","year":"1976","unstructured":"McCormick, G.P.: Computability of global solutions to factorable nonconvex programs: Part I\u2014convex underestimating problems. Math. Program. 10(1), 147\u2013175 (1976)","journal-title":"Math. Program."},{"issue":"1","key":"554_CR17","doi-asserted-by":"publisher","first-page":"e12","DOI":"10.5334\/jors.81","volume":"4","author":"AS Siqueira","year":"2016","unstructured":"Siqueira, A.S., da Silva, R.C., Santos, L.-R.: Perprof-py: a python package for performance profile of mathematical optimization software. J. Open Res. Softw. 4(1), e12 (2016)","journal-title":"J. Open Res. Softw."},{"key":"554_CR18","unstructured":"Telgarsky, M.: Representation benefits of deep feedforward networks. arxiv:https:\/\/arxiv.org\/abs\/1509.08101 (2015)"},{"key":"554_CR19","unstructured":"Wachter, A.: An interior point algorithm for large-scale nonlinear optimization with applications in process engineering. PhD thesis, Carnegie Mellon University (2002)"},{"key":"554_CR20","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.neunet.2017.07.002","volume":"94","author":"D Yarotsky","year":"2017","unstructured":"Yarotsky, D.: Error bounds for approximations with deep relu networks. Neural Netw. 94, 103\u2013114 (2017)","journal-title":"Neural Netw."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-024-00554-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10589-024-00554-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-024-00554-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,13]],"date-time":"2024-04-13T12:07:18Z","timestamp":1713010038000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10589-024-00554-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,18]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["554"],"URL":"https:\/\/doi.org\/10.1007\/s10589-024-00554-y","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"type":"print","value":"0926-6003"},{"type":"electronic","value":"1573-2894"}],"subject":[],"published":{"date-parts":[[2024,3,18]]},"assertion":[{"value":"2 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 March 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}