{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T02:43:52Z","timestamp":1782441832078,"version":"3.54.5"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,4,22]],"date-time":"2017-04-22T00:00:00Z","timestamp":1492819200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2017,4,22]],"date-time":"2017-04-22T00:00:00Z","timestamp":1492819200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000147","name":"National Science Foundation (NSF), Division of Civil, Mechanical and Manufacturing Innovation","doi-asserted-by":"publisher","award":["0856605"],"award-info":[{"award-number":["0856605"]}],"id":[{"id":"10.13039\/100000147","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000147","name":"National Science Foundation (NSF), Division of Civil, Mechanical and Manufacturing Innovation","doi-asserted-by":"publisher","award":["0900065"],"award-info":[{"award-number":["0900065"]}],"id":[{"id":"10.13039\/100000147","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000147","name":"National Science Foundation (NSF), Division of Civil, Mechanical and Manufacturing Innovation","doi-asserted-by":"publisher","award":["1234897"],"award-info":[{"award-number":["1234897"]}],"id":[{"id":"10.13039\/100000147","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000147","name":"National Science Foundation (NSF), Division of Civil, Mechanical and Manufacturing Innovation","doi-asserted-by":"publisher","award":["1235236"],"award-info":[{"award-number":["1235236"]}],"id":[{"id":"10.13039\/100000147","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.1007\/s10107-017-1138-3","type":"journal-article","created":{"date-parts":[[2017,4,22]],"date-time":"2017-04-22T14:48:27Z","timestamp":1492872507000},"page":"377-415","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Deriving convex hulls through lifting and projection"],"prefix":"10.1007","volume":"169","author":[{"given":"Trang T.","family":"Nguyen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Philippe P.","family":"Richard","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohit","family":"Tawarmalani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,4,22]]},"reference":[{"key":"1138_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, 273\u2013286 (1983)","journal-title":"Math. Oper. Res."},{"key":"1138_CR2","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s10107-010-0355-9","volume":"124","author":"KM Anstreicher","year":"2010","unstructured":"Anstreicher, K.M., Burer, S.: Computable representations for convex hulls of low-dimensional quadratic forms. Math. Program. 124, 33\u201343 (2010)","journal-title":"Math. Program."},{"key":"1138_CR3","doi-asserted-by":"crossref","unstructured":"Belotti, P., Miller, A., Namazifar, M.: Valid inequalities for sets defined by multilinear functions. In: Proceedings of the European Workshop on Mixed Integer Nonlinear Programming (2010)","DOI":"10.1016\/j.endm.2010.05.102"},{"key":"1138_CR4","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1137\/S0036144596302644","volume":"40","author":"JF Bonnans","year":"1998","unstructured":"Bonnans, J.F., Shapiro, A.: Optimization problems with perturbations: a guided tour. SIAM Rev. 40, 228\u2013264 (1998)","journal-title":"SIAM Rev."},{"key":"1138_CR5","doi-asserted-by":"crossref","unstructured":"Costa, A., Liberti, L.: Relaxations of multilinear convex envelopes: dual is better than primal. In Experimental Algorithms, pp. 87\u201398. Springer, Berlin, Heidelberg (2012)","DOI":"10.1007\/978-3-642-30850-5_9"},{"key":"1138_CR6","volume-title":"Inequalities","author":"GH Hardy","year":"1952","unstructured":"Hardy, G.H., Littlewood, J.E., P\u00f3lya, G.: Inequalities. Cambridge University Press, Cambridge (1952)"},{"key":"1138_CR7","doi-asserted-by":"publisher","first-page":"1451","DOI":"10.1137\/07069359X","volume":"19","author":"M Jach","year":"2008","unstructured":"Jach, M., Michaels, D., Weismantel, R.: The convex envelope of ($$n$$-1)-convex functions. SIAM J. Optim. 19, 1451\u20131466 (2008)","journal-title":"SIAM J. Optim."},{"key":"1138_CR8","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/s10107-011-0496-5","volume":"137","author":"A Khajavirad","year":"2013","unstructured":"Khajavirad, A., Sahinidis, N.V.: Convex envelopes generated from finitely many compact convex sets. Math. Program. 137, 371\u2013408 (2013)","journal-title":"Math. Program."},{"key":"1138_CR9","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/s10107-012-0616-x","volume":"144","author":"M Locatelli","year":"2014","unstructured":"Locatelli, M., Schoen, F.: On convex envelopes for bivariate functions over polytopes. Math. Program. 144, 65\u201391 (2014)","journal-title":"Math. Program."},{"key":"1138_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, 325\u2013351 (2012)","journal-title":"Math. Program."},{"key":"1138_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-convex underestimating problems. Math. Program. 10, 147\u2013175 (1976)","journal-title":"Math. Program."},{"key":"1138_CR12","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. Global Optim. 29, 125\u2013155 (2004)","journal-title":"J. Global Optim."},{"key":"1138_CR13","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/s10107-005-0580-9","volume":"103","author":"CA Meyer","year":"2005","unstructured":"Meyer, C.A., Floudas, C.A.: Convex envelopes for edge-concave functions. Math. Program. 103, 207\u2013224 (2005)","journal-title":"Math. Program."},{"key":"1138_CR14","unstructured":"Richard, J.-P.P., Tawarmalani, M.: MIP lifting techniques for mixed integer nonlinear programs. In: Third Workshop on Mixed Integer Programming, Miami (2006)"},{"key":"1138_CR15","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/s10107-008-0226-9","volume":"121","author":"J-PP Richard","year":"2010","unstructured":"Richard, J.-P.P., Tawarmalani, M.: Lifting inequalities: a framework for generating strong cuts for nonlinear programs. Math. Program. 121, 61\u2013104 (2010)","journal-title":"Math. Program."},{"key":"1138_CR16","volume-title":"Convex Analysis. Princeton Mathematical Series","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton Mathematical Series. Princeton University Press, Princeton (1970)"},{"key":"1138_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, 245\u2013270 (1997)","journal-title":"Acta Math. Vietnam."},{"key":"1138_CR18","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."},{"key":"1138_CR19","unstructured":"Tawarmalani, M., Richard, J.-P. P.: Decomposition techniques in convexification of inequalities. Krannert Working Paper (2015)"},{"key":"1138_CR20","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1023\/A:1011233805045","volume":"20","author":"M Tawarmalani","year":"2001","unstructured":"Tawarmalani, M., Sahinidis, N.V.: Semidefinite relaxations of fractional programs via novel techniques for constructing convex envelopes of nonlinear functions. J. Global Optim. 20, 137\u2013158 (2001)","journal-title":"J. Global Optim."},{"key":"1138_CR21","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.P., Chung, K.: Strong valid inequalities for orthogonal disjunctions and bilinear covering sets. Math. Program. 124, 481\u2013512 (2010)","journal-title":"Math. Program."},{"key":"1138_CR22","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.P., Xiong, C.: Explicit convex and concave envelopes through polyhedral subdivisions. Math. Program. 138, 531\u2013577 (2013)","journal-title":"Math. Program."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-017-1138-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-017-1138-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-017-1138-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T16:23:46Z","timestamp":1589646226000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-017-1138-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,22]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["1138"],"URL":"https:\/\/doi.org\/10.1007\/s10107-017-1138-3","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4,22]]},"assertion":[{"value":"28 February 2014","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2017","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 April 2017","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}