{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T17:26:55Z","timestamp":1778347615880,"version":"3.51.4"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,3,20]],"date-time":"2015-03-20T00:00:00Z","timestamp":1426809600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2015,6]]},"DOI":"10.1007\/s10107-015-0891-4","type":"journal-article","created":{"date-parts":[[2015,3,19]],"date-time":"2015-03-19T07:16:57Z","timestamp":1426749417000},"page":"191-223","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":83,"title":["On mathematical programming with indicator constraints"],"prefix":"10.1007","volume":"151","author":[{"given":"Pierre","family":"Bonami","sequence":"first","affiliation":[]},{"given":"Andrea","family":"Lodi","sequence":"additional","affiliation":[]},{"given":"Andrea","family":"Tramontani","sequence":"additional","affiliation":[]},{"given":"Sven","family":"Wiese","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,3,20]]},"reference":[{"key":"891_CR1","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1287\/mnsc.34.3.391","volume":"34","author":"J Adams","year":"1983","unstructured":"Adams, J., Balas, E., Zawack, D.: The shifting bottleneck procedure for job shop scheduling. Manag. Sci. 34, 391\u2013401 (1983)","journal-title":"Manag. Sci."},{"key":"891_CR2","unstructured":"Akt\u00fcrk, S., Atamt\u00fcrk, A., G\u00fcrel, S.: A strong conic quadratic reformulation for machine-job assignment with controllable processing times. Technical Report BCOL Research Report 07.01, Industrial Engineering and Operations Research, University of California, Berkeley (2007)"},{"key":"891_CR3","unstructured":"Ascheuer, N.: Hamiltonian Path Problems in the On-line Optimization of Flexible Manufacturing Systems. PhD thesis, Technische Universit\u00e4t Berlin (1995)"},{"key":"891_CR4","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0167-5060(08)70342-X","volume":"5","author":"E Balas","year":"1979","unstructured":"Balas, E.: Disjunctive programming. Ann. Discrete Math. 5, 3\u201351 (1979)","journal-title":"Ann. Discrete Math."},{"key":"891_CR5","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0166-218X(98)00136-X","volume":"89","author":"E Balas","year":"1998","unstructured":"Balas, E.: Disjunctive programming: properties of the convex hull of feasible points. Discrete Appl. Math. 89, 3\u201344 (1998)","journal-title":"Discrete Appl. Math."},{"key":"891_CR6","first-page":"259","volume":"58","author":"E Balas","year":"1993","unstructured":"Balas, E., Ceria, S., Cornu\u00e9jols, G.: A lift-and-project cutting plane algorithm for mixed 0\u20131 programs. Math. Program. 58, 259\u2013324 (1993)","journal-title":"Math. Program."},{"key":"891_CR7","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1287\/mnsc.42.9.1229","volume":"42","author":"E Balas","year":"1996","unstructured":"Balas, E., Ceria, S., Cornu\u00e9jols, G.: Mixed 0\u20131 programming by lift-and-project in a branch-and-cut framework. Manag. Sci. 42, 1229\u20131246 (1996)","journal-title":"Manag. Sci."},{"key":"891_CR8","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/0377-2217(80)90106-X","volume":"4","author":"E Balas","year":"1980","unstructured":"Balas, E., Jeroslow, R.: Strengthening cuts for mixed integer programs. Eur. J. Oper. Res. 4, 224\u2013234 (1980)","journal-title":"Eur. J. Oper. Res."},{"key":"891_CR9","unstructured":"Belotti, P., Bonami, P., Fischetti, M., Lodi, A., Monaci, M., Nogales-G\u00f3mez, A., Salvagnin, D.: On handling indicator constraints in mixed-integer programming. Technical Report OR\/13\/1, revised OR\/14\/20, DEI, University of Bologna (2014)"},{"key":"891_CR10","first-page":"1441","volume-title":"Wiley Encyclopedia of Operations Research and Management Science","author":"P Belotti","year":"2011","unstructured":"Belotti, P., Liberti, L., Lodi, A., Nannicini, G., Tramontani, A.: Disjunctive inequalities: applications and extensions. In: Cochran, J.J. (ed.) Wiley Encyclopedia of Operations Research and Management Science, vol. 2, pp. 1441\u20131450. Wiley, New York (2011)"},{"key":"891_CR11","first-page":"94","volume":"1","author":"W Ben-Ameur","year":"2006","unstructured":"Ben-Ameur, W., Ouorou, A.: Mathematical models of the delay-constrained routing problem. Algorithmic Oper. Res. 1, 94\u2013103 (2006)","journal-title":"Algorithmic Oper. Res."},{"key":"891_CR12","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/S0377-2217(99)00486-5","volume":"127","author":"J Bla\u017cewicz","year":"2000","unstructured":"Bla\u017cewicz, J., Pesch, E., Sterna, M.: The disjunctive graph machine representation of the job shop scheduling problem. Eur. J. Oper. Res. 127, 317\u2013331 (2000)","journal-title":"Eur. J. Oper. Res."},{"key":"891_CR13","first-page":"52","volume-title":"Integer Programming and Combinatorial Optimization, Volume 6655 of Lecture Notes in Computer Science","author":"P Bonami","year":"2011","unstructured":"Bonami, P.: Lift-and-project cuts for mixed integer convex programs. In: G\u00fcnl\u00fck, O., Woeginger, G. (eds.) Integer Programming and Combinatorial Optimization, Volume 6655 of Lecture Notes in Computer Science, pp. 52\u201364. Springer, Berlin (2011)"},{"key":"891_CR14","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/s12532-012-0037-0","volume":"4","author":"P Bonami","year":"2012","unstructured":"Bonami, P.: On optimizing over lift-and-project closures. Math. Program. Comput. 4, 151\u2013179 (2012)","journal-title":"Math. Program. Comput."},{"key":"891_CR15","first-page":"521","volume-title":"Progress in Combinatorial Optimization","author":"P Bonami","year":"2011","unstructured":"Bonami, P., Linderoth, J.T., Lodi, A.: Disjunctive cuts for mixed integer nonlinear programming problems. In: Majoub, R. (ed.) Progress in Combinatorial Optimization, pp. 521\u2013544. Wiley\/ISTE, New York (2011)"},{"key":"891_CR16","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1287\/opre.1100.0854","volume":"59","author":"JP Brooks","year":"2011","unstructured":"Brooks, J.P.: Support vector machines with the ramp loss and the hard margin loss. Oper. Res. 59, 467\u2013479 (2011)","journal-title":"Oper. Res."},{"key":"891_CR17","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1007\/s101070050106","volume":"86","author":"S Ceria","year":"1999","unstructured":"Ceria, S., Soares, J.: Convex programming for disjunctive convex optimization. Math. Program. 86, 595\u2013614 (1999)","journal-title":"Math. Program."},{"key":"891_CR18","unstructured":"Conjunctive Normal Form. In: Hazewinkel, M. (ed.) Encyclopedia of Mathematics. Springer, Berlin (2001)"},{"key":"891_CR19","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1287\/mnsc.23.8.789","volume":"23","author":"G Cornu\u00e9jols","year":"1977","unstructured":"Cornu\u00e9jols, G., Fisher, M.L., Nemhauser, G.L.: Location of bank accounts to optimize float: an analytic study of exact and approximate algorithms. Manag. Sci. 23, 789\u2013810 (1977)","journal-title":"Manag. Sci."},{"key":"891_CR20","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1287\/ijoc.1100.0432","volume":"24","author":"S Dash","year":"2012","unstructured":"Dash, S., G\u00fcnl\u00fck, O., Lodi, A., Tramontani, A.: A time bucket formulation for the traveling salesman problem with time windows. INFORMS J. Comput. 24, 132\u2013147 (2012)","journal-title":"INFORMS J. Comput."},{"key":"891_CR21","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1287\/msom.1050.0094","volume":"8","author":"S Elhedhli","year":"2006","unstructured":"Elhedhli, S.: Service system design with immobile servers, stochastic demand, and congestion. Manuf. Serv. Oper. Manag. 8, 92\u201397 (2006)","journal-title":"Manuf. Serv. Oper. Manag."},{"key":"891_CR22","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s10107-009-0300-y","volume":"128","author":"M Fischetti","year":"2011","unstructured":"Fischetti, M., Lodi, A., Tramontani, A.: On the separation of disjunctive cuts. Math. Program. 128, 205\u2013230 (2011)","journal-title":"Math. Program."},{"key":"891_CR23","first-page":"225","volume-title":"Industrial Scheduling","author":"H Fisher","year":"1963","unstructured":"Fisher, H., Thompson, G.L.: Probabilistic learning combinations of local job-shop scheduling rules. In: Muth, J.F., Thompson, G.L. (eds.) Industrial Scheduling, pp. 225\u2013251. Prentice-Hall, Englewood Cliffs (1963)"},{"key":"891_CR24","doi-asserted-by":"crossref","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 convex 0\u20131 mixed integer programs. Math. Program. 106, 225\u2013236 (2006)","journal-title":"Math. Program."},{"key":"891_CR25","unstructured":"Furman, K., Grossmann, I.E., Sawaya, N.: A useful algebraic representation of disjunctive convex sets using the perspective function. In: Conference talk MINLP, Pittsburgh (2014)"},{"key":"891_CR26","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1023\/A:1025154322278","volume":"26","author":"IE Grossmann","year":"2003","unstructured":"Grossmann, I.E., Lee, S.: Generalized convex disjunctive programming: nonlinear convex hull relaxation. Comput. Optim. Appl. 26, 83\u2013100 (2003)","journal-title":"Comput. Optim. Appl."},{"issue":"9","key":"891_CR27","doi-asserted-by":"crossref","first-page":"3276","DOI":"10.1002\/aic.14088","volume":"59","author":"IE Grossmann","year":"2013","unstructured":"Grossmann, I.E., Trespalacios, F.: Systematic modeling of discrete\u2013continuous optimization models through generalized disjunctive programming. AIChE J. 59(9), 3276\u20133295 (2013)","journal-title":"AIChE J."},{"key":"891_CR28","unstructured":"G\u00fcnl\u00fck, O., Lee, J., Weismantel, R.: MINLP strengthening for separaable convex quadratic transportation-cost UFL. Technical Report RC24213 (W0703\u2013042), IBM Research Division (2007)"},{"key":"891_CR29","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/978-1-4614-1927-3_3","volume-title":"Mixed Integer Nonlinear Programming, Volume 154 of The IMA Volumes in Mathematics and its Applications","author":"O G\u00fcnl\u00fck","year":"2012","unstructured":"G\u00fcnl\u00fck, O., Linderoth, J.: Perspective reformulation and applications. In: Lee, J., Leyffer, S. (eds.) Mixed Integer Nonlinear Programming, Volume 154 of The IMA Volumes in Mathematics and its Applications, pp. 61\u201389. Springer, New York (2012)"},{"key":"891_CR30","unstructured":"Hijazi, H.: Mixed-Integer Nonlinear Optimization Approaches for Network Design in Telecommunications. PhD thesis, Universit\u00e9 d\u2019Aix-Marseille II (2010)"},{"key":"891_CR31","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1007\/s10589-011-9424-0","volume":"52","author":"H Hijazi","year":"2012","unstructured":"Hijazi, H., Bonami, P., Cornu\u00e9jols, G., Ouorou, A.: Mixed integer nonlinear programs featuring \u201con\/off\u201d constraints. Comput. Optim. Appl. 52, 537\u2013558 (2012)","journal-title":"Comput. Optim. Appl."},{"key":"891_CR32","unstructured":"Hijazi, H., Liberti, L.: Constraint qualification failure in second-order cone formulations of unbounded disjunctions. Technical Report, NICTA, Canberra ACT Australia (2014)"},{"key":"891_CR33","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/BFb0121015","volume-title":"Mathematical Programming at Oberwolfach II, Volume 22 of Mathematical Programming Studies","author":"R Jeroslow","year":"1984","unstructured":"Jeroslow, R., Lowe, J.: Modelling with integer varibales. In: Korte, B., Ritter, K. (eds.) Mathematical Programming at Oberwolfach II, Volume 22 of Mathematical Programming Studies, pp. 167\u2013184. Springer, Berlin (1984)"},{"key":"891_CR34","unstructured":"K\u0131l\u0131n\u00e7, M.: Disjunctive Cutting Planes and Algorithms for Convex Mixed Integer Nonlinear Programming. PhD thesis, University of Wisconsin-Madison (2011)"},{"key":"891_CR35","unstructured":"K\u0131l\u0131n\u00e7, M., Linderoth, J., Luedtke, J.: Effective separation of disjunctive cuts for convex mixed integer nonlinear programs. Technical Report TR1681, Computer Sciences Department, University of Wisconsin-Madison (2010)"},{"key":"891_CR36","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s12532-011-0025-9","volume":"3","author":"T Koch","year":"2011","unstructured":"Koch, T., Achterberg, T., Andersen, E., Bastert, O., Berthold, T., Bixby, R.E., Danna, E., Gamrath, G., Gleixner, A.M., Heinz, S., Lodi, A., Mittelmann, H., Ralphs, T., Salvagnin, D., Steffy, D.E., Wolter, K.: Miplib 2010. Math. Program. Comput. 3, 103\u2013163 (2011)","journal-title":"Math. Program. Comput."},{"key":"891_CR37","volume-title":"Evaluating Gas Network Capacities. SIAM-MOS series on Optimization","year":"2014","unstructured":"Koch, T., Hiller, B., Pfetsch, M.E., Schewe, L. (eds.): Evaluating Gas Network Capacities. SIAM-MOS series on Optimization. SIAM, Philadelphia (2014)"},{"key":"891_CR38","volume-title":"Resource Constrained Project Scheduling: An Experimental Investigation of Heuristic Scheduling Techniques","author":"S Lawrence","year":"1984","unstructured":"Lawrence, S.: Resource Constrained Project Scheduling: An Experimental Investigation of Heuristic Scheduling Techniques. GSIA, Carnegie Mellon University, Pittsburgh (1984)"},{"key":"891_CR39","doi-asserted-by":"crossref","first-page":"2125","DOI":"10.1016\/S0098-1354(00)00581-0","volume":"24","author":"S Lee","year":"2000","unstructured":"Lee, S., Grossmann, I.E.: New algorithms for nonlinear generalized disjunctive programming. Comput. Chem. Eng. 24, 2125\u20132141 (2000)","journal-title":"Comput. Chem. Eng."},{"key":"891_CR40","unstructured":"Lodi, A.: Indicator constraints in mixed-integer programming. In: Conference Talk MIP, Columbus (2014)"},{"key":"891_CR41","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/978-3-540-68279-0_16","volume-title":"50 Years of Integer Programming 1958\u20132008","author":"A Lodi","year":"2010","unstructured":"Lodi, A.: Mixed integer programming computation. In: J\u00fcnger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G., Wolsey, L.A. (eds.) 50 Years of Integer Programming 1958\u20132008, pp. 619\u2013645. Springer, Berlin (2010)"},{"key":"891_CR42","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/s101070050103","volume":"86","author":"RA Stubbs","year":"1999","unstructured":"Stubbs, R.A., Mehrotra, S.: A branch-and-cut method for 0\u20131 mixed convex programming. Math. Program. 86, 515\u2013532 (1999)","journal-title":"Math. Program."},{"key":"891_CR43","unstructured":"Tramontani, A.: Lift-and-project cuts in CPLEX 12.5.1. In: Conference Talk INFORMS, Minneapolis (2013)"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-015-0891-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-015-0891-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-015-0891-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,22]],"date-time":"2019-08-22T04:15:33Z","timestamp":1566447333000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-015-0891-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,20]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,6]]}},"alternative-id":["891"],"URL":"https:\/\/doi.org\/10.1007\/s10107-015-0891-4","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,20]]}}}