{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T19:57:26Z","timestamp":1725479846147},"publisher-location":"Berlin, Heidelberg","reference-count":34,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642366932"},{"type":"electronic","value":"9783642366949"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-36694-9_26","type":"book-chapter","created":{"date-parts":[[2013,3,11]],"date-time":"2013-03-11T06:08:39Z","timestamp":1362982119000},"page":"302-313","source":"Crossref","is-referenced-by-count":0,"title":["Facial Structure and Representation of Integer Hulls of Convex Sets"],"prefix":"10.1007","author":[{"given":"Vishnu","family":"Narayanan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"26_CR1","unstructured":"Abhishek, K., Leyffer, S., Linderoth, J.: FilMINT: An outer-approximation-based solver for nonlinear mixed-integer programs. Preprint, Argonne National Laboratory, Mathematics and Computer Science Division, Argonne, IL (2006)"},{"key":"26_CR2","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/j.disopt.2009.03.002","volume":"6","author":"A. Atamt\u00fcrk","year":"2009","unstructured":"Atamt\u00fcrk, A., Narayanan, V.: The submodular knapsack polytope. Discrete Optimization\u00a06, 333\u2013344 (2009)","journal-title":"Discrete Optimization"},{"key":"26_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10107-008-0239-4","volume":"122","author":"A. Atamt\u00fcrk","year":"2010","unstructured":"Atamt\u00fcrk, A., Narayanan, V.: Conic mixed-integer rounding cuts. Mathematical Programming\u00a0122, 1\u201320 (2010)","journal-title":"Mathematical Programming"},{"key":"26_CR4","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1007\/s10107-009-0282-9","volume":"126","author":"A. Atamt\u00fcrk","year":"2011","unstructured":"Atamt\u00fcrk, A., Narayanan, V.: Lifting for conic mixed-integer programming. Mathematical Programming\u00a0126, 351\u2013363 (2011)","journal-title":"Mathematical Programming"},{"key":"26_CR5","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1080\/10556780903087124","volume":"24","author":"P. Belotti","year":"2009","unstructured":"Belotti, P., Lee, J., Libreti, L., Margot, F., Waechter, A.: Branching and bound tightening techniques for non-convex MINLP. Optimization Methods and Software\u00a024, 597\u2013634 (2009)","journal-title":"Optimization Methods and Software"},{"key":"26_CR6","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/j.disopt.2006.10.011","volume":"5","author":"P. Bonami","year":"2008","unstructured":"Bonami, P., Biegler, L.T., Conn, A.R., Cornu\u00e9jols, G., Grossmann, I.E., Laird, C.D., Lee, J., Lodi, A., Margot, F., Sawaya, N., Waechter, A.: An algorithmic framework for convex mixed-integer nonlinear programs. Discrete Optimization\u00a05, 186\u2013204 (2008)","journal-title":"Discrete Optimization"},{"key":"26_CR7","series-title":"IMA Volumes in Mathematics and its Applications","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-1-4614-1927-3_1","volume-title":"Mixed Integer Nonlinear Programming","author":"P. Bonami","year":"2012","unstructured":"Bonami, P., Kilin\u00e7, M., Linderoth, J.: Algorithms and software for convex mixed integer nonlinear programs. In: Lee, J., Leyffer, S. (eds.) Mixed Integer Nonlinear Programming. IMA Volumes in Mathematics and its Applications, vol.\u00a0154, pp. 1\u201339. Springer, New York (2012)"},{"key":"26_CR8","unstructured":"Braun, G., Pokutta, S.: A short proof of the polyhedrality of the chv\u00e1tal-gomory closure of a compact set (2012)"},{"key":"26_CR9","doi-asserted-by":"crossref","unstructured":"Burer, S., Letchford, A.: Unbounded convex sets for non-convex mixed-integer quadratic programming. Mathematical Programming (2012) (to appear)","DOI":"10.1007\/s10107-012-0609-9"},{"key":"26_CR10","doi-asserted-by":"crossref","unstructured":"Cassels, J.W.: An Introduction to the Geometry of Numbers. Springer (1997)","DOI":"10.1007\/978-3-642-62035-5_3"},{"key":"26_CR11","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/s10107-005-0578-3","volume":"104","author":"M. \u00c7ezik","year":"2005","unstructured":"\u00c7ezik, M., Iyengar, G.: Cuts for mixed 0\u20131 conic programming. Mathematical Programming\u00a0104, 179\u2013202 (2005)","journal-title":"Mathematical Programming"},{"key":"26_CR12","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1287\/moor.1110.0488","volume":"36","author":"D. Dadush","year":"2011","unstructured":"Dadush, D., Dey, S., Vielma, J.: The Chv\u00e1tal-Gomory closure of a strictly convex body. Mathematics of Operations Research\u00a036, 227\u2013239 (2011a)","journal-title":"Mathematics of Operations Research"},{"key":"26_CR13","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/j.orl.2011.02.002","volume":"39","author":"D. Dadush","year":"2011","unstructured":"Dadush, D., Dey, S., Vielma, J.: The split closure of a strictly convex body. Operations Research Letters\u00a039, 121\u2013126 (2011b)","journal-title":"Operations Research Letters"},{"key":"26_CR14","doi-asserted-by":"crossref","unstructured":"Dadush, D., Dey, S., Vielma, J.: On the Chv\u00e1tal-Gomory closure of a compact convex set (2012), arXiv:1011.1710v1 (math.OC)","DOI":"10.1007\/s10107-013-0649-9"},{"key":"26_CR15","doi-asserted-by":"crossref","unstructured":"Dey, S., Mor\u00e1n R., D.A.: Some properties of convex hulls of integer points contained in general convex sets. Mathematical Programming Online First, doi: 10.1007\/s10107-012-0538-7","DOI":"10.1007\/s10107-012-0538-7"},{"key":"26_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/978-3-642-13036-6_25","volume-title":"Integer Programming and Combinatorial Optimization","author":"S.S. Dey","year":"2010","unstructured":"Dey, S.S., Vielma, J.P.: The Chv\u00e1tal-Gomory Closure of an Ellipsoid Is a Polyhedron. In: Eisenbrand, F., Shepherd, F.B. (eds.) IPCO 2010. LNCS, vol.\u00a06080, pp. 327\u2013340. Springer, Heidelberg (2010)"},{"key":"26_CR17","doi-asserted-by":"crossref","unstructured":"Dunkel, J., Schulz, A.: The Gomory-Chv\u00e1tal closure of a non-rational polytope is a rational polytope. Mathematics of Operations Research (to appear), doi:10.1287\/moor.1120.0565","DOI":"10.1287\/moor.1120.0565"},{"issue":"1","key":"26_CR18","first-page":"139","volume":"25","author":"V.P. Fedotov","year":"1979","unstructured":"Fedotov, V.P.: Isolated faces of a convex compactum. Mathematicheskie Zametki\u00a025(1), 139\u2013147 (1979)","journal-title":"Mathematicheskie Zametki"},{"key":"26_CR19","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s10107-005-0594-3","volume":"106","author":"A. Frangioni","year":"2006","unstructured":"Frangioni, A., Gentile, C.: Perspective cuts for a class of 0\u20131 mixed integer programs. Mathematical Programming\u00a0106, 225\u2013236 (2006)","journal-title":"Mathematical Programming"},{"key":"26_CR20","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1007\/s00454-003-0782-y","volume":"29","author":"M. Gr\u00f6tschel","year":"2003","unstructured":"Gr\u00f6tschel, M., Henk, M.: The representation of polyhedra by polynomial inequalities. Discrete and Comuputational Geometry\u00a029, 485\u2013504 (2003)","journal-title":"Discrete and Comuputational Geometry"},{"key":"26_CR21","unstructured":"G\u00fcnl\u00fck, O., Lee, J., Weismantel, R.: MINLP strengthening for separable convex quadratic transportation-cost UFL. IBM Research Report RC24213, IBM, Yorktown Heights, NY (March 2007)"},{"key":"26_CR22","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/s10107-010-0360-z","volume":"104","author":"O. G\u00fcnl\u00fck","year":"2010","unstructured":"G\u00fcnl\u00fck, O., Linderoth, J.: Perspective relaxation of mixed integer nonlinear programs with indicator variables. Mathematical Programming, Series B\u00a0104, 183\u2013206 (2010)","journal-title":"Mathematical Programming, Series B"},{"key":"26_CR23","doi-asserted-by":"crossref","unstructured":"Hiriart-Urruty, J., Lemar\u00e9chal, C.: Fundamentals of Convex Analysis. Grundlehren Text edn. Springer Heidelberg (2001)","DOI":"10.1007\/978-3-642-56468-0"},{"issue":"1","key":"26_CR24","first-page":"131","volume":"46","author":"D.A. Jaume","year":"2005","unstructured":"Jaume, D.A., Puente, R.: Conjugacy for closed convex sets. Contributions to Algebra and Geometry\u00a046(1), 131\u2013149 (2005)","journal-title":"Contributions to Algebra and Geometry"},{"key":"26_CR25","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1007\/BF01899998","volume":"8","author":"V. Klee","year":"1957","unstructured":"Klee, V.: Extremal structure of convex sets. Archiv der Mathematik\u00a08, 234\u2013240 (1957)","journal-title":"Archiv der Mathematik"},{"key":"26_CR26","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/BF01585518","volume":"7","author":"R. Meyer","year":"1974","unstructured":"Meyer, R.: On the existence of optimal solutions to integer and mixed-integer programming problems. Mathematical Programming\u00a07, 223\u2013235 (1974)","journal-title":"Mathematical Programming"},{"key":"26_CR27","doi-asserted-by":"crossref","unstructured":"Mor\u00e1n R., D.A., Dey, S.S., Vielma, J.P.: A strong dual for conic mixed-integer programs. SIAM Journal on Optimization 22, 1136\u20131150 (2012)","DOI":"10.1137\/110840868"},{"issue":"5","key":"26_CR28","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1023\/A:1021106512173","volume":"115","author":"J.O. Moussafir","year":"2003","unstructured":"Moussafir, J.O.: Convex hulls of integral points. Journal of Mathematical Sciences\u00a0115(5), 647\u2013665 (2003)","journal-title":"Journal of Mathematical Sciences"},{"issue":"2","key":"26_CR29","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1287\/moor.1060.0242","volume":"32","author":"G. Pataki","year":"2007","unstructured":"Pataki, G.: On the closedness of the linear image of a closed convex cone. Mathematics of Operations Research\u00a032(2), 395\u2013412 (2007)","journal-title":"Mathematics of Operations Research"},{"key":"26_CR30","series-title":"Princeton Landmarks in Mathematics","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"R.T. Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton Landmarks in Mathematics. Princeton University Press, Princeton (1970)"},{"key":"26_CR31","volume-title":"Variational Analysis","author":"R.T. Rockafellar","year":"2004","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational Analysis. Springer, Berlin (2004)"},{"issue":"3","key":"26_CR32","doi-asserted-by":"publisher","first-page":"482","DOI":"10.2478\/s11533-008-0038-4","volume":"6","author":"E. Schmutz","year":"2008","unstructured":"Schmutz, E.: Rational points on the unit sphere. Central European Journal of Mathematics\u00a06(3), 482\u2013487 (2008)","journal-title":"Central European Journal of Mathematics"},{"key":"26_CR33","doi-asserted-by":"crossref","unstructured":"Schneider, R.: Convex Bodies: The Brunn-Minkowski Theory. Cambridge University Press (1993)","DOI":"10.1017\/CBO9780511526282"},{"key":"26_CR34","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/s101070050103","volume":"86","author":"R. Stubbs","year":"1999","unstructured":"Stubbs, R., Mehrotra, S.: A branch-and-cut method for 0-1 mixed convex programming. Mathematical Programming\u00a086, 515\u2013532 (1999)","journal-title":"Mathematical Programming"}],"container-title":["Lecture Notes in Computer Science","Integer Programming and Combinatorial Optimization"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-36694-9_26","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,11]],"date-time":"2019-05-11T13:45:26Z","timestamp":1557582326000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-36694-9_26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642366932","9783642366949"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-36694-9_26","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}