{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T15:44:57Z","timestamp":1725464697010},"publisher-location":"Berlin, Heidelberg","reference-count":30,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642308499"},{"type":"electronic","value":"9783642308505"}],"license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-30850-5_8","type":"book-chapter","created":{"date-parts":[[2012,5,28]],"date-time":"2012-05-28T01:44:33Z","timestamp":1338169473000},"page":"75-86","source":"Crossref","is-referenced-by-count":0,"title":["Compact Relaxations for Polynomial Programming Problems"],"prefix":"10.1007","author":[{"given":"Sonia","family":"Cafieri","sequence":"first","affiliation":[]},{"given":"Pierre","family":"Hansen","sequence":"additional","affiliation":[]},{"given":"Lucas","family":"L\u00e9tocart","sequence":"additional","affiliation":[]},{"given":"Leo","family":"Liberti","sequence":"additional","affiliation":[]},{"given":"Fr\u00e9d\u00e9ric","family":"Messine","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"2","key":"8_CR1","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/s10898-004-0864-2","volume":"33","author":"L. Liberti","year":"2005","unstructured":"Liberti, L.: Linearity embedded in nonconvex programs. Journal of Global Optimization\u00a033(2), 157\u2013196 (2005)","journal-title":"Journal of Global Optimization"},{"key":"8_CR2","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10898-006-9005-4","volume":"36","author":"L. Liberti","year":"2006","unstructured":"Liberti, L., Pantelides, C.: An exact reformulation algorithm for large nonconvex NLPs involving bilinear terms. Journal of Global Optimization\u00a036, 161\u2013189 (2006)","journal-title":"Journal of Global Optimization"},{"issue":"3","key":"8_CR3","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s10288-006-0015-3","volume":"5","author":"L. Liberti","year":"2007","unstructured":"Liberti, L.: Compact linearization of binary quadratic problems. 4OR\u00a05(3), 231\u2013245 (2007)","journal-title":"4OR"},{"key":"8_CR4","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/BF00122429","volume":"2","author":"H. Sherali","year":"1992","unstructured":"Sherali, H., Alameddine, A.: A new reformulation-linearization technique for bilinear programming problems. Journal of Global Optimization\u00a02, 379\u2013410 (1992)","journal-title":"Journal of Global Optimization"},{"key":"8_CR5","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/BF00121304","volume":"2","author":"H. Sherali","year":"1991","unstructured":"Sherali, H., Tuncbilek, C.: A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique. Journal of Global Optimization\u00a02, 101\u2013112 (1991)","journal-title":"Journal of Global Optimization"},{"key":"8_CR6","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1007\/PL00011409","volume":"89","author":"H. Sherali","year":"2001","unstructured":"Sherali, H., Wang, H.: Global optimization of nonconvex factorable programming problems. Mathematical Programming\u00a089, 459\u2013478 (2001)","journal-title":"Mathematical Programming"},{"key":"8_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0167-6377(97)00013-8","volume":"21","author":"H. Sherali","year":"1997","unstructured":"Sherali, H., Tuncbilek, C.: New reformulation linearization\/convexification relaxations for univariate and multivariate polynomial programming problems. Operations Research Letters\u00a021, 1\u20139 (1997)","journal-title":"Operations Research Letters"},{"key":"8_CR8","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1007\/s10898-011-9757-3","volume":"52","author":"H. Sherali","year":"2012","unstructured":"Sherali, H., Dalkiran, E., Liberti, L.: Reduced RLT representations for nonconvex polynomial programming problems. Journal of Global Optimization\u00a052, 447\u2013469 (2012)","journal-title":"Journal of Global Optimization"},{"key":"8_CR9","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/BF01580665","volume":"10","author":"G. McCormick","year":"1976","unstructured":"McCormick, G.: Computability of global solutions to factorable nonconvex programs: Part I \u2014 Convex underestimating problems. Mathematical Programming\u00a010, 146\u2013175 (1976)","journal-title":"Mathematical Programming"},{"issue":"2","key":"8_CR10","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1287\/moor.8.2.273","volume":"8","author":"F. Al-Khayyal","year":"1983","unstructured":"Al-Khayyal, F., Falk, J.: Jointly constrained biconvex programming. Mathematics of Operations Research\u00a08(2), 273\u2013286 (1983)","journal-title":"Mathematics of Operations Research"},{"key":"8_CR11","doi-asserted-by":"crossref","unstructured":"Jiao, Y., Stillinger, F., Torquato, S.: Geometrical ambiguity of pair statistics I. point configurations. Technical Report 0908.1366v1, arXiv (2009)","DOI":"10.1103\/PhysRevE.81.011105"},{"issue":"4","key":"8_CR12","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1023\/A:1008217604285","volume":"10","author":"A. Rikun","year":"1997","unstructured":"Rikun, A.: A convex envelope formula for multilinear functions. Journal of Global Optimization\u00a010(4), 425\u2013437 (1997)","journal-title":"Journal of Global Optimization"},{"key":"8_CR13","unstructured":"Christof, T., L\u00f6bel, A.: The porta manual page. Technical Report v.\u00a01.4.0, ZIB, Berlin (1997)"},{"key":"8_CR14","unstructured":"Avis, D.: User\u2019s Guide for lrs (2009)"},{"key":"8_CR15","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. Computers & Chemical Engineering\u00a023, 457\u2013478 (1999)","journal-title":"Computers & Chemical Engineering"},{"issue":"9","key":"8_CR16","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1016\/S0098-1354(98)00027-1","volume":"22","author":"C. Adjiman","year":"1998","unstructured":"Adjiman, C., Dallwig, S., Floudas, C., Neumaier, A.: A global optimization method, \u03b1BB, for general twice-differentiable constrained NLPs: I. Theoretical advances. Computers & Chemical Engineering\u00a022(9), 1137\u20131158 (1998)","journal-title":"Theoretical advances. Computers & Chemical Engineering"},{"key":"8_CR17","unstructured":"Sahinidis, N., Tawarmalani, M.: BARON 7.2.5: Global Optimization of Mixed-Integer Nonlinear Programs, User\u2019s Manual (2005)"},{"key":"8_CR18","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/0-387-30528-9_8","volume-title":"Global Optimization: from Theory to Implementation","author":"L. Liberti","year":"2006","unstructured":"Liberti, L.: Writing global optimization software. In: Liberti, L., Maculan, N. (eds.) Global Optimization: from Theory to Implementation, pp. 211\u2013262. Springer, Heidelberg (2006)"},{"issue":"4","key":"8_CR19","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. Optimization Methods and Software\u00a024(4), 597\u2013634 (2009)","journal-title":"Optimization Methods and Software"},{"key":"8_CR20","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1007\/s10898-009-9484-1","volume":"47","author":"S. Cafieri","year":"2010","unstructured":"Cafieri, S., Lee, J., Liberti, L.: On convex relaxations of quadrilinear terms. Journal of Global Optimization\u00a047, 661\u2013685 (2010)","journal-title":"Journal of Global Optimization"},{"key":"8_CR21","first-page":"327","volume-title":"Frontiers in Global Optimization","author":"C. Meyer","year":"2003","unstructured":"Meyer, C., Floudas, C.: Trilinear monomials with positive or negative domains: Facet s of the convex and concave envelopes. In: Floudas, C., Pardalos, P. (eds.) Frontiers in Global Optimization, pp. 327\u2013352. Kluwer Academic Publishers, Amsterdam (2003)"},{"key":"8_CR22","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1023\/B:JOGO.0000042112.72379.e6","volume":"29","author":"C. Meyer","year":"2004","unstructured":"Meyer, C., Floudas, C.: Trilinear monomials with mixed sign domains: Facets of the convex and concave envelopes. Journal of Global Optimization\u00a029, 125\u2013155 (2004)","journal-title":"Journal of Global Optimization"},{"key":"8_CR23","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1023\/A:1021924706467","volume":"25","author":"L. Liberti","year":"2003","unstructured":"Liberti, L., Pantelides, C.: Convex envelopes of monomials of odd degree. Journal of Global Optimization\u00a025, 157\u2013168 (2003)","journal-title":"Journal of Global Optimization"},{"key":"8_CR24","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717716","volume-title":"Introduction to Interval Analysis","author":"R. Moore","year":"2009","unstructured":"Moore, R., Kearfott, R., Cloud, M.: Introduction to Interval Analysis. SIAM, Philadelphia (2009)"},{"key":"8_CR25","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s10801-005-4531-6","volume":"22","author":"M. Katzman","year":"2005","unstructured":"Katzman, M.: Counting monomials. Journal of Algebraic Combinatorics\u00a022, 331\u2013341 (2005)","journal-title":"Journal of Algebraic Combinatorics"},{"issue":"6","key":"8_CR26","first-page":"589","volume":"4","author":"F. Messine","year":"1998","unstructured":"Messine, F., Lagouanelle, J.: Enclosure methods for multivariate differentiable functions and application to global optimization. Journal of Universal Computer Science\u00a04(6), 589\u2013603 (1998)","journal-title":"Journal of Universal Computer Science"},{"key":"8_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/978-3-642-17458-2_7","volume-title":"Combinatorial Optimization and Applications","author":"P. Belotti","year":"2010","unstructured":"Belotti, P., Cafieri, S., Lee, J., Liberti, L.: Feasibility-Based Bounds Tightening via Fixed Points. In: Wu, W., Daescu, O. (eds.) COCOA 2010, Part I. LNCS, vol.\u00a06508, pp. 65\u201376. Springer, Heidelberg (2010)"},{"key":"8_CR28","doi-asserted-by":"publisher","first-page":"842","DOI":"10.1073\/pnas.43.9.842","volume":"43","author":"C. Berge","year":"1957","unstructured":"Berge, C.: Two theorems in graph theory. Proceedings of the National Academy of Science of the U.S.\u00a043, 842\u2013844 (1957)","journal-title":"Proceedings of the National Academy of Science of the U.S."},{"key":"8_CR29","volume-title":"Combinatorial Optimization: Algorithms and Complexity","author":"C. Papadimitriou","year":"1998","unstructured":"Papadimitriou, C., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover, New York (1998)"},{"key":"8_CR30","unstructured":"ILOG: ILOG CPLEX 11.0 User\u2019s Manual. ILOG S.A., Gentilly, France (2008)"}],"container-title":["Lecture Notes in Computer Science","Experimental Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-30850-5_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T01:03:27Z","timestamp":1558314207000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-30850-5_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642308499","9783642308505"],"references-count":30,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-30850-5_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}