{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T07:38:04Z","timestamp":1761896284302,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2016,5,30]],"date-time":"2016-05-30T00:00:00Z","timestamp":1464566400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,5,30]],"date-time":"2016-05-30T00:00:00Z","timestamp":1464566400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["LP110200524"],"award-info":[{"award-number":["LP110200524"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2017,3]]},"DOI":"10.1007\/s10107-016-1031-5","type":"journal-article","created":{"date-parts":[[2016,5,30]],"date-time":"2016-05-30T11:28:04Z","timestamp":1464607684000},"page":"523-535","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Bounding the gap between the McCormick relaxation and the convex hull for bilinear functions"],"prefix":"10.1007","volume":"162","author":[{"given":"Natashia","family":"Boland","sequence":"first","affiliation":[]},{"given":"Santanu S.","family":"Dey","sequence":"additional","affiliation":[]},{"given":"Thomas","family":"Kalinowski","sequence":"additional","affiliation":[]},{"given":"Marco","family":"Molinaro","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6088-1511","authenticated-orcid":false,"given":"Fabian","family":"Rigterink","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,5,30]]},"reference":[{"issue":"2","key":"1031_CR1","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1287\/moor.8.2.273","volume":"8","author":"FA Al-Khayyal","year":"1983","unstructured":"Al-Khayyal, F.A., Falk, J.E.: Jointly constrained biconvex programming. Math. Oper. Res. 8(2), 273\u2013286 (1983)","journal-title":"Math. Oper. Res."},{"issue":"4\u20135","key":"1031_CR2","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1080\/10556780903087124","volume":"24","author":"P Belotti","year":"2009","unstructured":"Belotti, P., Lee, J., Liberti, L., Margot, F., W\u00e4chter, A.: Branching and bounds tightening techniques for non-convex MINLP. Optim. Methods Softw. 24(4\u20135), 597\u2013634 (2009)","journal-title":"Optim. Methods Softw."},{"key":"1031_CR3","doi-asserted-by":"crossref","unstructured":"Bollob\u00e1s, B., Scott, A.D.: Discrepancy in graphs and hypergraphs. In: Gy\u00f6ry, E., Katona, G.O.H., Lov\u00e1sz, L. (eds.) Bolyai Society Mathematical Studies, pp. 33\u201356. Springer, Berlin (2006)","DOI":"10.1007\/978-3-540-32439-3_3"},{"key":"1031_CR4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626371","volume-title":"The Discrepancy Method. Randomness and Complexity","author":"B Chazelle","year":"2000","unstructured":"Chazelle, B.: The Discrepancy Method. Randomness and Complexity. Cambridge University Press, Cambridge (2000)"},{"issue":"1\u20133","key":"1031_CR5","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/BF01582138","volume":"61","author":"Y Crama","year":"1993","unstructured":"Crama, Y.: Concave extensions for nonlinear $$0-1$$ maximization problems. Math. Program. 61(1\u20133), 53\u201360 (1993)","journal-title":"Math. Program."},{"issue":"4","key":"1031_CR6","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1002\/net.3230010407","volume":"1","author":"P Erd\u0151s","year":"1971","unstructured":"Erd\u0151s, P., Spencer, J.: Imbalances in k-colorations. Networks 1(4), 379\u2013385 (1971)","journal-title":"Networks"},{"issue":"1","key":"1031_CR7","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1002\/jgt.3190120113","volume":"12","author":"P Erd\u0151s","year":"1988","unstructured":"Erd\u0151s, P., Goldberg, M., Pach, J., Spencer, J.: Cutting a graph into two dissimilar halves. J. Graph Theory 12(1), 121\u2013131 (1988)","journal-title":"J. Graph Theory"},{"issue":"3","key":"1031_CR8","doi-asserted-by":"crossref","first-page":"231","DOI":"10.4064\/sm-70-3-231-283","volume":"70","author":"U Haagerup","year":"1981","unstructured":"Haagerup, U.: The best constants in the Khintchine inequality. Stud. Math. 70(3), 231\u2013283 (1981)","journal-title":"Stud. Math."},{"key":"1031_CR9","volume-title":"Global Optimization: Deterministic Approaches","author":"R Horst","year":"2013","unstructured":"Horst, R., Tuy, H.: Global Optimization: Deterministic Approaches, 3rd edn. Springer, Berlin (2013)","edition":"3"},{"issue":"2","key":"1031_CR10","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s10107-012-0606-z","volume":"136","author":"J Luedtke","year":"2012","unstructured":"Luedtke, J., Namazifar, M., Linderoth, J.: Some results on the strength of relaxations of multilinear functions. Math. Program. 136(2), 325\u2013351 (2012)","journal-title":"Math. Program."},{"issue":"1","key":"1031_CR11","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":"1031_CR12","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1080\/10556788.2014.916287","volume":"30","author":"R Misener","year":"2014","unstructured":"Misener, R., Smadbeck, J.B., Floudas, C.A.: Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2. Optim. Methods Softw. 30(1), 215\u2013249 (2014)","journal-title":"Optim. Methods Softw."},{"key":"1031_CR13","doi-asserted-by":"crossref","unstructured":"Nazarov, F.L., Podkorytov, A.N.: Ball, Haagerup, and distribution functions. In: Havin, V.P., Nikolski, N.K. (eds.) Complex Analysis, Operators, and Related Topics, pp. 247\u2013267. Springer, Berlin (2000)","DOI":"10.1007\/978-3-0348-8378-8_21"},{"key":"1031_CR14","unstructured":"Nikolov, A.: Combinatorial discrepancy of the system of all cuts. Theoretical Computer Science Stack Exchange. \n                    http:\/\/cstheory.stackexchange.com\/q\/32072cstheory.stackexchange.com\/q\/32072\n                    \n                   (version: July 26, 2015)"},{"issue":"4","key":"1031_CR15","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1023\/A:1008217604285","volume":"10","author":"AD Rikun","year":"1997","unstructured":"Rikun, A.D.: A convex envelope formula for multilinear functions. J. Glob. Optim. 10(4), 425\u2013437 (1997)","journal-title":"J. Glob. Optim."},{"issue":"2","key":"1031_CR16","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/BF00138693","volume":"8","author":"NV Sahinidis","year":"1996","unstructured":"Sahinidis, N.V.: BARON: a general purpose global optimization software package. J. Glob. Optim. 8(2), 201\u2013205 (1996)","journal-title":"J. Glob. Optim."},{"issue":"1","key":"1031_CR17","first-page":"245","volume":"22","author":"HD Sherali","year":"1997","unstructured":"Sherali, H.D.: Convex envelopes of multilinear functions over a unit hypercube and over special discrete sets. Acta Math. Vietnam. 22(1), 245\u2013270 (1997)","journal-title":"Acta Math. Vietnam."},{"issue":"4\u20135","key":"1031_CR18","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/S0098-1354(98)00286-5","volume":"23","author":"E Smith","year":"1999","unstructured":"Smith, E., Pantelides, C.: A symbolic reformulation\/spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs. Comput. Chem. Eng. 23(4\u20135), 457\u2013478 (1999)","journal-title":"Comput. Chem. Eng."},{"key":"1031_CR19","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1007\/s10107-012-0581-4","volume":"138","author":"M Tawarmalani","year":"2012","unstructured":"Tawarmalani, M., Richard, J.-P., Xiong, C.: Explicit convex and concave envelopes through polyhedral subdivisions. Math. Program. 138, 531\u2013577 (2012)","journal-title":"Math. Program."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-1031-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-016-1031-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-1031-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-1031-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T16:20:03Z","timestamp":1589646003000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-016-1031-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,30]]},"references-count":19,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2017,3]]}},"alternative-id":["1031"],"URL":"https:\/\/doi.org\/10.1007\/s10107-016-1031-5","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"type":"print","value":"0025-5610"},{"type":"electronic","value":"1436-4646"}],"subject":[],"published":{"date-parts":[[2016,5,30]]},"assertion":[{"value":"30 July 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 May 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 May 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}