{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T07:37:33Z","timestamp":1761896253861,"version":"3.37.3"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,1,14]],"date-time":"2016-01-14T00:00:00Z","timestamp":1452729600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft (DE)","doi-asserted-by":"publisher","award":["STE 772\/14-1"],"award-info":[{"award-number":["STE 772\/14-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2016,6]]},"DOI":"10.1007\/s10957-016-0862-9","type":"journal-article","created":{"date-parts":[[2016,1,14]],"date-time":"2016-01-14T19:29:24Z","timestamp":1452799764000},"page":"1079-1109","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques"],"prefix":"10.1007","volume":"169","author":[{"given":"Peter","family":"Kirst","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oliver","family":"Stein","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,1,14]]},"reference":[{"key":"862_CR1","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1137\/1035089","volume":"35","author":"R Hettich","year":"1993","unstructured":"Hettich, R., Kortanek, K.O.: Semi-infinite programming: theory, methods, and applications. SIAM Rev. 35, 380\u2013429 (1993)","journal-title":"SIAM Rev."},{"key":"862_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-322-93108-5","volume-title":"Numerische Methoden der Approximation und Semi-infiniten Optimierung","author":"R Hettich","year":"1982","unstructured":"Hettich, R., Zencke, P.: Numerische Methoden der Approximation und Semi-infiniten Optimierung. Teubner, Stuttgart (1982)"},{"key":"862_CR3","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/978-1-4757-2868-2_7","volume-title":"Semi-Infinite Programming","author":"R Reemtsen","year":"1998","unstructured":"Reemtsen, R., G\u00f6rner, S.: Numerical methods for semi-infinite programming: a survey. In: Reemtsen, R., R\u00fcckmann, J.-J. (eds.) Semi-Infinite Programming, pp. 195\u2013275. Kluwer, Boston (1998)"},{"key":"862_CR4","volume-title":"Linear Semi-infinite Optimization","author":"MA Goberna","year":"1998","unstructured":"Goberna, M.A., L\u00f3pez, M.A.: Linear Semi-infinite Optimization. Wiley, Chichester (1998)"},{"key":"862_CR5","volume-title":"Optimization. Algorithms and Consistent Approximations","author":"E Polak","year":"1997","unstructured":"Polak, E.: Optimization. Algorithms and Consistent Approximations. Springer, Berlin (1997)"},{"key":"862_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9164-5","volume-title":"Bi-level Strategies in Semi-infinite Programming","author":"O Stein","year":"2003","unstructured":"Stein, O.: Bi-level Strategies in Semi-infinite Programming. Kluwer, Boston (2003)"},{"key":"862_CR7","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.cam.2007.02.012","volume":"217","author":"FG V\u00e1zquez","year":"2008","unstructured":"V\u00e1zquez, F.G., R\u00fcckmann, J.-J., Stein, O., Still, G.: Generalized semi-infinite programming: a tutorial. J. Comput. Appl. Math. 217, 394\u2013419 (2008)","journal-title":"J. Comput. Appl. Math."},{"key":"862_CR8","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/j.ejor.2006.08.045","volume":"180","author":"M L\u00f3pez","year":"2007","unstructured":"L\u00f3pez, M., Still, G.: Semi-infinite programming. Eur. J. Oper. Res. 180, 491\u2013518 (2007)","journal-title":"Eur. J. Oper. Res."},{"key":"862_CR9","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1016\/j.ejor.2012.06.009","volume":"223","author":"O Stein","year":"2012","unstructured":"Stein, O.: How to solve a semi-infinite optimization problem. Eur. J. Oper. Res. 223, 312\u2013320 (2012)","journal-title":"Eur. J. Oper. Res."},{"key":"862_CR10","doi-asserted-by":"crossref","DOI":"10.1002\/9781118627372","volume-title":"Integer and Combinatorial Optimization","author":"GL Nemhauser","year":"1988","unstructured":"Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, New York (1988)"},{"key":"862_CR11","volume-title":"Model Building in Mathematical Programming","author":"HP Williams","year":"1978","unstructured":"Williams, H.P.: Model Building in Mathematical Programming. Wiley, Chichester (1978)"},{"key":"862_CR12","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1093\/comjnl\/8.3.250","volume":"8","author":"RJ Dakin","year":"1965","unstructured":"Dakin, R.J.: A tree-search algorithm for mixed integer programming problems. Comput. J. 8, 250\u2013255 (1965)","journal-title":"Comput. J."},{"key":"862_CR13","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":"862_CR14","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":"862_CR15","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/S0166-218X(01)00340-7","volume":"123","author":"E Balas","year":"2002","unstructured":"Balas, E., Perregaard, M.: Lift-and-project for mixed 0\u20131 programming: recent progress. Discrete Appl. Math. 123, 129\u2013154 (2002)","journal-title":"Discrete Appl. Math."},{"key":"862_CR16","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1016\/0377-2217(90)90419-C","volume":"46","author":"N Beaumont","year":"1990","unstructured":"Beaumont, N.: An algorithm for disjunctive programs. Eur. J. Oper. Res. 46, 362\u2013371 (1990)","journal-title":"Eur. J. Oper. Res."},{"key":"862_CR17","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/S0166-218X(99)00100-6","volume":"96\u201397","author":"JN Hooker","year":"1999","unstructured":"Hooker, J.N., Osorio, M.A.: Mixed logical-linear programming. Discrete Appl. Math. 96\u201397, 395\u2013442 (1999)","journal-title":"Discrete Appl. Math."},{"key":"862_CR18","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0098-1354(91)87007-V","volume":"15","author":"R Raman","year":"1991","unstructured":"Raman, R., Grossmann, I.E.: Relations between MILP modelling and logical inference for chemical process synthesis. Comput. Chem. Eng. 15, 73\u201384 (1991)","journal-title":"Comput. Chem. Eng."},{"key":"862_CR19","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1016\/0098-1354(93)80073-V","volume":"17","author":"R Raman","year":"1993","unstructured":"Raman, R., Grossmann, I.E.: Symbolic integration of logic in mixed-integer linear programming techniques for process synthesis. Comput. Chem. Eng. 17, 909\u2013927 (1993)","journal-title":"Comput. Chem. Eng."},{"key":"862_CR20","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1023\/A:1021039126272","volume":"3","author":"IE Grossmann","year":"2002","unstructured":"Grossmann, I.E.: Review of nonlinear mixed-integer and disjunctive programming techniques. Optim. Eng. 3, 227\u2013252 (2002)","journal-title":"Optim. Eng."},{"key":"862_CR21","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/BF02592064","volume":"36","author":"MA Duran","year":"1986","unstructured":"Duran, M.A., Grossmann, I.E.: An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math. Program. 36, 307\u2013339 (1986)","journal-title":"Math. Program."},{"key":"862_CR22","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/BF01581153","volume":"66","author":"R Fletcher","year":"1994","unstructured":"Fletcher, R., Leyffer, S.: Solving mixed integer nonlinear programs by outer approximation. Math. Program. 66, 327\u2013349 (1994)","journal-title":"Math. Program."},{"key":"862_CR23","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0098-1354(95)87027-X","volume":"19","author":"T Westerlund","year":"1995","unstructured":"Westerlund, T., Pettersson, F.: An extended cutting plane method for solving convex MINLP problems. Comput. Chem. Eng. 19, 131\u2013136 (1995)","journal-title":"Comput. Chem. Eng."},{"key":"862_CR24","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."},{"key":"862_CR25","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":"862_CR26","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1023\/A:1022650006477","volume":"93","author":"HTh Jongen","year":"1997","unstructured":"Jongen, HTh, R\u00fcckmann, J.-J., Stein, O.: Disjunctive optimization: critical point theory. J. Optim. Theory Appl. 93, 321\u2013336 (1997)","journal-title":"J. Optim. Theory Appl."},{"key":"862_CR27","doi-asserted-by":"crossref","first-page":"1675","DOI":"10.1016\/S0098-1354(01)00732-3","volume":"25","author":"S Lee","year":"2001","unstructured":"Lee, S., Grossmann, I.E.: A global optimization algorithm for nonconvex generalized disjunctive programming and applications to process systems. Comput. Chem. Eng. 25, 1675\u20131697 (2001)","journal-title":"Comput. Chem. Eng."},{"key":"862_CR28","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1023\/A:1008245113420","volume":"13","author":"E Levitin","year":"1998","unstructured":"Levitin, E., Tichatschke, R.: A branch-and-bound approach for solving a class of generalized semi-infinite programming problems. J. Glob. Optim. 13, 299\u2013315 (1998)","journal-title":"J. Glob. Optim."},{"key":"862_CR29","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s10589-012-9489-4","volume":"54","author":"M Diehl","year":"2013","unstructured":"Diehl, M., Houska, B., Stein, O., Steuermann, P.: A lifting method for generalized semi-infinite programs based on lower level Wolfe duality. Comput. Optim. Appl. 54, 189\u2013210 (2013)","journal-title":"Comput. Optim. Appl."},{"key":"862_CR30","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1016\/S0377-2217(01)00307-1","volume":"142","author":"O Stein","year":"2002","unstructured":"Stein, O., Still, G.: On generalized semi-infinite optimization and bilevel optimization. Eur. J. Oper. Res. 142, 444\u2013462 (2002)","journal-title":"Eur. J. Oper. Res."},{"key":"862_CR31","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2836-1","volume-title":"Practical Bilevel Optimization","author":"JF Bard","year":"1998","unstructured":"Bard, J.F.: Practical Bilevel Optimization. Kluwer, Dordrecht (1998)"},{"key":"862_CR32","volume-title":"Foundations of Bilevel Programming","author":"S Dempe","year":"2002","unstructured":"Dempe, S.: Foundations of Bilevel Programming. Kluwer, Dordrecht (2002)"},{"key":"862_CR33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1287\/moor.25.1.1.15213","volume":"25","author":"H Scheel","year":"2000","unstructured":"Scheel, H., Scholtes, S.: Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Math. Oper. Res. 25, 1\u201322 (2000)","journal-title":"Math. Oper. Res."},{"key":"862_CR34","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1137\/S0363012901398393","volume":"42","author":"O Stein","year":"2003","unstructured":"Stein, O., Still, G.: Solving semi-infinite optimization problems with interior point techniques. SIAM J. Control Optim. 42, 769\u2013788 (2003)","journal-title":"SIAM J. Control Optim."},{"key":"862_CR35","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s101070050048","volume":"85","author":"F Facchinei","year":"1999","unstructured":"Facchinei, F., Jiang, H., Qi, L.: A smoothing method for mathematical programs with equilibrium constraints. Math. Program. 85, 107\u2013134 (1999)","journal-title":"Math. Program."},{"key":"862_CR36","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/s10957-010-9674-5","volume":"146","author":"O Stein","year":"2010","unstructured":"Stein, O., Winterfeld, A.: A feasible method for generalized semi-infinite programming. J. Optim. Theory Appl. 146, 419\u2013443 (2010)","journal-title":"J. Optim. Theory Appl."},{"key":"862_CR37","volume-title":"Nonlinear Programming","author":"MS Bazaraa","year":"2013","unstructured":"Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming. Wiley, New York (2013)"},{"key":"862_CR38","first-page":"299","volume":"79","author":"J-S Pang","year":"1997","unstructured":"Pang, J.-S.: Error bounds in mathematical programming. Math. Program. 79, 299\u2013332 (1997)","journal-title":"Math. Program."},{"key":"862_CR39","volume-title":"Asymptotic Cones and Functions in Optimization and Variational Inequalities","author":"A Auslender","year":"2003","unstructured":"Auslender, A., Teboulle, M.: Asymptotic Cones and Functions in Optimization and Variational Inequalities. Springer, New York (2003)"},{"key":"862_CR40","doi-asserted-by":"crossref","unstructured":"Az\u00e9, D.: A survey on error bounds for lower semicontinuous functions. In: Proceedings of 2003 MODE-SMAI Conference, EDP Sci., Les Ulis, pp. 1\u201317 (2003)","DOI":"10.1051\/proc:2003004"},{"key":"862_CR41","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A W\u00e4chter","year":"2006","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106, 25\u201357 (2006)","journal-title":"Math. Program."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-0862-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-016-0862-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-0862-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T05:58:46Z","timestamp":1559455126000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-016-0862-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,14]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,6]]}},"alternative-id":["862"],"URL":"https:\/\/doi.org\/10.1007\/s10957-016-0862-9","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2016,1,14]]}}}