{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T22:03:09Z","timestamp":1770415389504,"version":"3.49.0"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T00:00:00Z","timestamp":1565049600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T00:00:00Z","timestamp":1565049600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Prog. Comp."],"published-print":{"date-parts":[[2020,6]]},"DOI":"10.1007\/s12532-019-00169-z","type":"journal-article","created":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:03:42Z","timestamp":1565107422000},"page":"165-191","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["On the impact of running intersection inequalities for globally solving polynomial optimization problems"],"prefix":"10.1007","volume":"12","author":[{"given":"Alberto","family":"Del Pia","sequence":"first","affiliation":[]},{"given":"Aida","family":"Khajavirad","sequence":"additional","affiliation":[]},{"given":"Nikolaos V.","family":"Sahinidis","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,8,6]]},"reference":[{"issue":"1","key":"169_CR1","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/s10107-016-1032-4","volume":"162","author":"M Anthony","year":"2017","unstructured":"Anthony, M., Boros, E., Crama, Y., Gruber, A.: Quadratic reformulations of nonlinear binary optimization problems. Math. Program. 162(1), 115\u2013144 (2017). \nhttps:\/\/doi.org\/10.1007\/s10107-016-1032-4","journal-title":"Math. Program."},{"key":"169_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12532-014-0073-z","volume":"7","author":"X Bao","year":"2015","unstructured":"Bao, X., Khajavirad, A., Sahinidis, N.V., Tawarmalani, M.: Global optimization of nonconvex problems with multilinear intermediates. Math. Program. Comput. 7, 1\u201337 (2015)","journal-title":"Math. Program. Comput."},{"key":"169_CR3","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/BF01587084","volume":"44","author":"F Barahona","year":"1989","unstructured":"Barahona, F., J\u00fcnger, M., Reinelt, G.: Experiments in quadratic $$0-1$$ programming. Math. Program. 44, 127\u2013137 (1989)","journal-title":"Math. Program."},{"key":"169_CR4","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1145\/2402.322389","volume":"30","author":"C Beeri","year":"1983","unstructured":"Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. J. ACM 30, 479\u2013513 (1983)","journal-title":"J. ACM"},{"key":"169_CR5","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, 597\u2013634 (2009)","journal-title":"Optim. Methods Softw."},{"key":"169_CR6","unstructured":"Berthold, T., Gamrath, G., Hendel, G., Heinz, S., Koch, T., Pfetsch, M., Vigerske, S., Waniek, R., Winkler, M., Wolter, K.: SCIP 3.2, User\u2019s Manual (2016)"},{"issue":"2","key":"169_CR7","doi-asserted-by":"publisher","first-page":"1121","DOI":"10.1137\/15M1054079","volume":"28","author":"D Bienstock","year":"2018","unstructured":"Bienstock, D., Munoz, G.: LP furmulations for polynomial optimization problems. SIAM J. Optim. 28(2), 1121\u20131150 (2018)","journal-title":"SIAM J. Optim."},{"key":"169_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-018-0133-x","author":"P Bonami","year":"2018","unstructured":"Bonami, P., G\u00fcnl\u00fck, O., Linderoth, J.: Globally solving nonconvex quadratic programming problems with box constraints via integer programming methods. Math. Program. Comput. (2018). \nhttps:\/\/doi.org\/10.1007\/s12532-018-0133-x","journal-title":"Math. Program. Comput."},{"key":"169_CR9","doi-asserted-by":"publisher","first-page":"1398","DOI":"10.1137\/050646500","volume":"18","author":"C Buchheim","year":"2007","unstructured":"Buchheim, C., Rinaldi, G.: Efficient reduction of polynomial zero-one optimization to the quadratic case. SIAM J. Optim. 18, 1398\u20131413 (2007)","journal-title":"SIAM J. Optim."},{"key":"169_CR10","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1007\/BF01582138","volume":"61","author":"Y Crama","year":"1993","unstructured":"Crama, Y.: Concave extensions for non-linear $$0-1$$ maximization problems. Math. Program. 61, 53\u201360 (1993)","journal-title":"Math. Program."},{"key":"169_CR11","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.disopt.2017.02.001","volume":"25","author":"Y Crama","year":"2017","unstructured":"Crama, Y., Rodr\u00edguez-Heck, E.: A class of valid inequalities for multilinear $$0-1$$ optimization problems. Discrete Optim. 25, 28\u201347 (2017)","journal-title":"Discrete Optim."},{"issue":"2","key":"169_CR12","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1287\/moor.2016.0804","volume":"42","author":"A Del Pia","year":"2017","unstructured":"Del Pia, A., Khajavirad, A.: A polyhedral study of binary polynomial programs. Math. Oper. Res. 42(2), 389\u2013410 (2017)","journal-title":"Math. Oper. Res."},{"key":"169_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-017-1158-z","author":"A Del Pia","year":"2017","unstructured":"Del Pia, A., Khajavirad, A.: On decomposability of multilinear sets. Math. Program. (2017). \nhttps:\/\/doi.org\/10.1007\/s10107-017-1158-z","journal-title":"Math. Program."},{"key":"169_CR14","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1137\/16M1095998","volume":"28","author":"A Del Pia","year":"2018","unstructured":"Del Pia, A., Khajavirad, A.: The multilinear polytope for acyclic hypergraphs. SIAM J. Optim. 28, 1049\u20131076 (2018)","journal-title":"SIAM J. Optim."},{"key":"169_CR15","unstructured":"Del\u00a0Pia, A., Khajavirad, A.: The running intersection relaxation of the multilinear polytope. Optim. Online manuscript 2018\/05\/6618 (2018)"},{"key":"169_CR16","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"E Dolan","year":"2002","unstructured":"Dolan, E., More, J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201\u2013213 (2002)","journal-title":"Math. Program."},{"key":"169_CR17","doi-asserted-by":"publisher","unstructured":"Fix, A., Gruber, A., Boros, E., Zabih, R.: A graph cut algorithm for higher-order Markov random fields. In: 2011 International Conference on Computer Vision, pp. 1020\u20131027 (2011). \nhttps:\/\/doi.org\/10.1109\/ICCV.2011.6126347","DOI":"10.1109\/ICCV.2011.6126347"},{"key":"169_CR18","unstructured":"GAMS Performance tools. Available at \nhttp:\/\/www.gams.com\/help\/topic\/gams.doc\/solvers\/allsolvers.pdf"},{"key":"169_CR19","first-page":"291","volume":"82","author":"C Helmberg","year":"1998","unstructured":"Helmberg, C., Rendl, F.: Solving quadratic $$0-1$$ problems by semidefinite programs and cutting planes. Math. Program. 82, 291\u2013315 (1998)","journal-title":"Math. Program."},{"key":"169_CR20","unstructured":"IBM: CPLEX Optimizer (2016). \nhttp:\/\/www-01.ibm.com\/software\/integration\/optimization\/cplex-optimizer\/"},{"key":"169_CR21","doi-asserted-by":"crossref","unstructured":"Karp, R.M.: Reducibility among combinatorial problems. In: Millera, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations. New York (1972)","DOI":"10.1007\/978-1-4684-2001-2_9"},{"key":"169_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-018-0138-5","author":"A Khajavirad","year":"2018","unstructured":"Khajavirad, A., Sahinidis, N.V.: A hybrid LP\/NLP paradigm for global optimization relaxations. Math. Program. Comput. (2018). \nhttps:\/\/doi.org\/10.1007\/s12532-018-0138-5","journal-title":"Math. Program. Comput."},{"key":"169_CR23","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1080\/10556780902753221","volume":"24","author":"Y Lin","year":"2009","unstructured":"Lin, Y., Schrage, L.: The global solver in the LINDO API. Optim. Methods Softw. 24, 657\u2013668 (2009)","journal-title":"Optim. Methods Softw."},{"key":"169_CR24","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-convex underestimating problems. Math. Program. 10, 147\u2013175 (1976)","journal-title":"Math. Program."},{"key":"169_CR25","first-page":"327","volume-title":"Frontiers in Global Optimization","author":"CA Meyer","year":"2003","unstructured":"Meyer, C.A., Floudas, C.A.: Trilinear monomials with positive or negative domains: facets of the convex and concave envelopes. In: Floudas, C.A., Pardolos, P.M. (eds.) Frontiers in Global Optimization, vol. 103, pp. 327\u2013352. Kluwer Academic Publishers, Norwell (2003)"},{"key":"169_CR26","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1023\/B:JOGO.0000042112.72379.e6","volume":"29","author":"CA Meyer","year":"2004","unstructured":"Meyer, C.A., Floudas, C.A.: Trilinear monomials with mixed sign domains: facets of the convex and concave envelopes. J. Glob. Optim. 29, 125\u2013155 (2004)","journal-title":"J. Glob. Optim."},{"key":"169_CR27","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/s10898-014-0166-2","volume":"59","author":"R Misener","year":"2014","unstructured":"Misener, R., Floudas, C.A.: ANTIGONE: algorithms for continuous\/integer global optimization of nonlinear equations. J. Glob. Optim. 59, 503\u2013526 (2014)","journal-title":"J. Glob. Optim."},{"key":"169_CR28","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/BF01589101","volume":"45","author":"M Padberg","year":"1989","unstructured":"Padberg, M.: The boolean quadric polytope: some characteristics, facets and relatives. Math. Program. 45, 139\u2013172 (1989)","journal-title":"Math. Program."},{"key":"169_CR29","unstructured":"POLIP: Library for polynomially constrained mixed-integer programming (2014). \nhttp:\/\/polip.zib.de"},{"key":"169_CR30","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, 425\u2013437 (1997)","journal-title":"J. Glob. Optim."},{"key":"169_CR31","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1023\/A:1011295715398","volume":"19","author":"HS Ryoo","year":"2001","unstructured":"Ryoo, H.S., Sahinidis, N.V.: Analysis of bounds for multilinear functions. J. Glob. Optim. 19, 403\u2013424 (2001)","journal-title":"J. Glob. Optim."},{"key":"169_CR32","unstructured":"Sahinidis, N.: Sahinidis optimization group website. \nhttp:\/\/archimedes.cheme.cmu.edu\/?q=baron"},{"key":"169_CR33","volume-title":"Theory of Linear and Integer Programming","author":"A Schrijver","year":"1986","unstructured":"Schrijver, A.: Theory of Linear and Integer Programming. Wiley, Chichester (1986)"},{"key":"169_CR34","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, 245\u2013270 (1997)","journal-title":"Acta Math. Vietnam."},{"key":"169_CR35","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1137\/0403036","volume":"3","author":"HD Sherali","year":"1990","unstructured":"Sherali, H.D., Adams, W.P.: A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Discrete Math. 3, 411\u2013430 (1990)","journal-title":"SIAM J. Discrete Math."},{"issue":"3","key":"169_CR36","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1137\/0213035","volume":"13","author":"RE Tarjan","year":"1984","unstructured":"Tarjan, R.E., Yannakakis, M.: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput. 13(3), 566\u2013579 (1984)","journal-title":"SIAM J. Comput."},{"key":"169_CR37","unstructured":"Tawarmalani, M.: Inclusion certificates and simultaneous convexification of functions. Working paper (2010). \nhttp:\/\/www.optimization-online.org\/DB_FILE\/2010\/09\/2722.pdf"},{"key":"169_CR38","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1007\/s10107-010-0374-6","volume":"124","author":"M Tawarmalani","year":"2010","unstructured":"Tawarmalani, M., Richard, J.P., Chung, K.: Strong valid inequalities for orthogonal disjunctions and bilinear covering sets. Math. Program. 124, 481\u2013512 (2010)","journal-title":"Math. Program."},{"key":"169_CR39","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1007\/s10107-012-0581-4","volume":"138","author":"M Tawarmalani","year":"2013","unstructured":"Tawarmalani, M., Richard, J.P., Xiong, C.: Explicit convex and concave envelopes through polyhedral subdivisions. Math. Program. 138, 531\u2013577 (2013)","journal-title":"Math. Program."},{"key":"169_CR40","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1007\/s10107-003-0467-6","volume":"99","author":"M Tawarmalani","year":"2004","unstructured":"Tawarmalani, M., Sahinidis, N.V.: Global optimization of mixed-integer nonlinear programs: a theoretical and computational study. Math. Program. 99, 563\u2013591 (2004)","journal-title":"Math. Program."},{"key":"169_CR41","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s10107-005-0581-8","volume":"103","author":"M Tawarmalani","year":"2005","unstructured":"Tawarmalani, M., Sahinidis, N.V.: A polyhedral branch-and-cut approach to global optimization. Math. Program. 103, 225\u2013249 (2005)","journal-title":"Math. Program."},{"key":"169_CR42","unstructured":"The Optimization Firm, LLC: NLP and MINLP test problems. \nhttps:\/\/minlp.com\/nlp-and-minlp-test-problems"},{"key":"169_CR43","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1023\/A:1008293029350","volume":"13","author":"Y Yajima","year":"1998","unstructured":"Yajima, Y., Fujie, T.: A polyhedral approach for nonconvex quadratic programming problems with box constraints. J. Glob. Optim. 13, 151\u2013170 (1998)","journal-title":"J. Glob. Optim."}],"container-title":["Mathematical Programming Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-019-00169-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12532-019-00169-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12532-019-00169-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,4]],"date-time":"2020-08-04T23:16:33Z","timestamp":1596582993000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12532-019-00169-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,6]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["169"],"URL":"https:\/\/doi.org\/10.1007\/s12532-019-00169-z","relation":{},"ISSN":["1867-2949","1867-2957"],"issn-type":[{"value":"1867-2949","type":"print"},{"value":"1867-2957","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,6]]},"assertion":[{"value":"30 June 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 July 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}