{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T00:02:27Z","timestamp":1783641747523,"version":"3.55.0"},"reference-count":55,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2007,12,5]],"date-time":"2007-12-05T00:00:00Z","timestamp":1196812800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2008,12]]},"DOI":"10.1007\/s10898-007-9260-z","type":"journal-article","created":{"date-parts":[[2007,12,6]],"date-time":"2007-12-06T11:20:09Z","timestamp":1196940009000},"page":"475-513","source":"Crossref","is-referenced-by-count":117,"title":["Global solution of bilevel programs with a nonconvex inner program"],"prefix":"10.1007","volume":"42","author":[{"given":"Alexander","family":"Mitsos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Panayiotis","family":"Lemonidis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul I.","family":"Barton","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2007,12,5]]},"reference":[{"issue":"1-2","key":"9260_CR1","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/S0377-0427(00)00342-3","volume":"121","author":"G. Alefeld","year":"2000","unstructured":"Alefeld G. and Mayer G. (2000). Interval analysis: theory and applications. J. Comput. Appl. Math. 121(1-2): 421\u2013464","journal-title":"J. Comput. Appl. Math."},{"key":"9260_CR2","volume-title":"Non-Linear Parametric Optimization","author":"B. Bank","year":"1983","unstructured":"Bank B., Guddat J., Klatte D., Kummer B. and Tammer K. (1983). Non-Linear Parametric Optimization. Birkh\u00e4user Verlag, Stuttgart"},{"issue":"2","key":"9260_CR3","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1287\/moor.8.2.260","volume":"8","author":"J.F. Bard","year":"1983","unstructured":"Bard J.F. (1983). An algorithm for solving the general bilevel programming problem. Math. Oper. Res. 8(2): 260\u2013272","journal-title":"Math. Oper. Res."},{"key":"9260_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2836-1","volume-title":"Practical Bilevel Optimization: Algorithms and Applications. Nonconvex Optimization and Its Applications","author":"J.F. Bard","year":"1998","unstructured":"Bard J.F. (1998). Practical Bilevel Optimization: Algorithms and Applications. Nonconvex Optimization and Its Applications. Kluwer Academic Publishers, Dordrecht"},{"key":"9260_CR5","volume-title":"Nonlinear Programming","author":"D.P. Bertsekas","year":"1999","unstructured":"Bertsekas D.P. (1999). Nonlinear Programming, 2nd edn. Athena Scientific, Belmont, Massachusetts","edition":"2"},{"key":"9260_CR6","volume-title":"Introduction to Linear Optimization","author":"D. Bertsimas","year":"1997","unstructured":"Bertsimas D. and Tsitsiklis J.N. (1997). Introduction to Linear Optimization. Athena Scientific, Belmont, Massachusetts"},{"issue":"1","key":"9260_CR7","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s10589-005-4556-8","volume":"30","author":"B. Bhattacharjee","year":"2005","unstructured":"Bhattacharjee B., Barton P.I. and Green W.H. Jr. (2005). Interval methods for semi-infinite programs. Comput. Optim. Appl. 30(1): 63\u201393","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"9260_CR8","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s10107-005-0583-6","volume":"103","author":"B. Bhattacharjee","year":"2005","unstructured":"Bhattacharjee B., Lemonidis P., Barton P.I. and Green W.H. Jr. (2005). Global solution of semi-infinite programs. Math. Program. Ser. B 103(2): 283\u2013307","journal-title":"Math. Program. Ser. B"},{"issue":"2","key":"9260_CR9","first-page":"261","volume":"19","author":"J.W. Blankenship","year":"1976","unstructured":"Blankenship J.W. and Falk J.E. (1976). Infinitely constrained optimization problems. J. Optim. Theory Appl. 19(2): 261\u2013281","journal-title":"Theory Appl."},{"issue":"1","key":"9260_CR10","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1287\/opre.21.1.37","volume":"21","author":"J. Bracken","year":"1973","unstructured":"Bracken J. and McGill J.T. (1973). Mathematical programs with optimization problems in constraints. Oper. Res. 21(1): 37\u201344","journal-title":"Oper. Res."},{"key":"9260_CR11","volume-title":"GAMS: A User\u2019s Guide","author":"A. Brooke","year":"1988","unstructured":"Brooke A., Kendrick D. and Meeraus A. (1988). GAMS: A User\u2019s Guide. The Scientific Press, Redwood City, California"},{"issue":"4","key":"9260_CR12","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1137\/0914049","volume":"14","author":"P.H. Calamai","year":"1993","unstructured":"Calamai P.H. and Vicente L.N. (1993). Generating linear and linear-quadratic bilevel programming-problems. SIAM J. Sci. Comput. 14(4): 770\u2013782","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"9260_CR13","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1145\/174603.174411","volume":"20","author":"P.H. Calamai","year":"1994","unstructured":"Calamai P.H. and Vicente L.N. (1994). Generating quadratic bilevel programming test problems. ACM Trans. Math. Software 20(1): 103\u2013119","journal-title":"ACM Trans. Math. Software"},{"issue":"2","key":"9260_CR14","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/BF01582148","volume":"61","author":"P.H. Calamai","year":"1993","unstructured":"Calamai P.H., Vicente L.N. and Judice J.J. (1993). A new technique for generating quadratic-programming test problems. Math. Program. 61(2): 215\u2013231","journal-title":"Program."},{"key":"9260_CR15","unstructured":"Colson, B.: BIPA (Bilevel programming with approximation methods): Software guide and test problems, Technical Report CRT-2002-38. Technical Report, Centre de Recherche sur les Transports, Universit\u00e9 de Montr\u00e9al, Montr\u00e9al, QC, Canada (2002)"},{"issue":"3","key":"9260_CR16","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s10589-005-4612-4","volume":"30","author":"B. Colson","year":"2005","unstructured":"Colson B., Marcotte P. and Savard G. (2005). A trust-region method for nonlinear bilevel programming: Algorithm and computational experience. Comput. Optim. Appl. 30(3): 211\u2013227","journal-title":"Optim. Appl."},{"key":"9260_CR17","volume-title":"Foundations of Bilevel Programming. Nonconvex Optimization and its Applications","author":"S. Dempe","year":"2002","unstructured":"Dempe S. (2002). Foundations of Bilevel Programming. Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Dordrecht"},{"issue":"3","key":"9260_CR18","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1080\/0233193031000149894","volume":"52","author":"S. Dempe","year":"2003","unstructured":"Dempe S. (2003). Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization 52(3): 333\u2013359","journal-title":"Optimization"},{"issue":"1","key":"9260_CR19","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/21.101139","volume":"21","author":"T.A. Edmunds","year":"1991","unstructured":"Edmunds T.A. and Bard J.F. (1991). Algorithms for nonlinear bilevel mathematical programs. IEEE Trans. Syst. Man Cybernet. 21(1): 83\u201389","journal-title":"IEEE Trans. Syst. Man Cybernet."},{"issue":"3","key":"9260_CR20","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1002\/nav.3800240307","volume":"24","author":"J.E. Falk","year":"1997","unstructured":"Falk J.E. and Hoffman K. (1997). A nonconvex max-min problem. Naval Res. Logist. 24(3): 441\u2013450","journal-title":"Naval Res. Logist."},{"issue":"1","key":"9260_CR21","first-page":"47","volume":"70","author":"J.E. Falk","year":"1995","unstructured":"Falk J.E. and Liu J.M. (1995). On bilevel programming, part I: general nonlinear cases. Math.Program. 70(1): 47\u201372","journal-title":"Math.Program."},{"issue":"20","key":"9260_CR22","doi-asserted-by":"crossref","first-page":"4267","DOI":"10.1021\/ie001014g","volume":"40","author":"C.A. Floudas","year":"2001","unstructured":"Floudas C.A., G\u00fcm\u00fcs Z.H. and Ierapetritou M.G. (2001). Global optimization in design under uncertainty: feasibility test and flexibility index problems. Indust. Eng. Chem. Res. 40(20): 4267\u20134282","journal-title":"Indust. Eng. Chem. Res."},{"issue":"4","key":"9260_CR23","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1137\/060657741","volume":"18","author":"C.A. Floudas","year":"2007","unstructured":"Floudas C.A. and Stein O. (2007). The adaptive convexification algorithm: a feasible point method for semi-infinite programming. SIAM J. Optim. 18(4): 1187\u20131208","journal-title":"SIAM J. Optim."},{"issue":"9","key":"9260_CR24","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1057\/jors.1981.156","volume":"32","author":"J. Fortuny-Amat","year":"1981","unstructured":"Fortuny-Amat J. and McCarl B. (1981). A representation and economic interpretation of a two-level programming problem. J. Oper. Res. Soc. 32(9): 783\u2013792","journal-title":"J. Oper. Res. Soc."},{"issue":"4","key":"9260_CR25","first-page":"455","volume":"22","author":"F. Glover","year":"1975","unstructured":"Glover F. (1975). Improved linear integer programming formulations of nonlinear integer programs. Manag. Sci. 22(4): 455\u2013460","journal-title":"Sci."},{"issue":"3","key":"9260_CR26","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1023\/A:1021039126272","volume":"3","author":"I.E. Grossmann","year":"2002","unstructured":"Grossmann I.E. (2002). Review of nonlinear mixed-integer and disjunctive programming techniques. Optim. Eng. 3(3): 227\u2013252","journal-title":"Optim. Eng."},{"issue":"4","key":"9260_CR27","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1002\/aic.690280422","volume":"28","author":"I.E. Grossmann","year":"1982","unstructured":"Grossmann I.E. and Halemane K.P. (1982). Decomposition strategy for designing flexible chemical-plants. AIChE J. 28(4): 686\u2013694","journal-title":"AIChE J."},{"issue":"1","key":"9260_CR28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1011268113791","volume":"20","author":"Z.H. G\u00fcm\u00fcs","year":"2001","unstructured":"G\u00fcm\u00fcs Z.H. and Floudas C.A. (2001). Global optimization of nonlinear bilevel programming problems. J. Glob. Optim. 20(1): 1\u201331","journal-title":"J. Glob. Optim."},{"issue":"1","key":"9260_CR29","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF00939768","volume":"58","author":"R. Horst","year":"1988","unstructured":"Horst R. (1988). Deterministic global optimization with partition sets whose feasibility is not known: application to concave minimization, reverse convex constraints, DC-programming and Lipschitzian optimization. J. Optim. Theo Appl. 58(1): 11\u201337","journal-title":"J. Optim. Theo Appl."},{"key":"9260_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03199-5","volume-title":"Global Optimization: Deterministic Approaches","author":"R. Horst","year":"1996","unstructured":"Horst R. and Tuy H. (1996). Global Optimization: Deterministic Approaches, 3rd edn. Springer, Berlin","edition":"3"},{"issue":"3","key":"9260_CR31","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1007\/s10107-004-0503-1","volume":"100","author":"P. Kesavan","year":"2004","unstructured":"Kesavan P., Allgor R.J., Gatzke E.P. and Barton P.I. (2004). Outer approximation algorithms for separable nonconvex mixed-integer nonlinear programs. Math. Program. 100(3): 517\u2013535","journal-title":"Math. Program."},{"issue":"2\u20137","key":"9260_CR32","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1016\/S0098-1354(00)00421-X","volume":"24","author":"P. Kesavan","year":"2000","unstructured":"Kesavan P. and Barton P.I. (2000). Generalized branch-and-cut framework for mixed-integer nonlinear optimization problems. Comput. Chem. Eng. 24(2\u20137): 1361\u20131366","journal-title":"Comput. Chem. Eng."},{"key":"9260_CR33","unstructured":"Lemonidis, P., Barton, P.I.: Global solution of generalized semi-infinite programs (In preparation)"},{"key":"9260_CR34","unstructured":"Lemonidis, P., Barton, P.I.: Interval methods for generalized semi-infinite programs. In: International Conference on Parametric Optimization and Related Topics (PARAOPT VIII), Cairo, Egypt, Nov. 27\u2013Dec. 1 2005"},{"key":"9260_CR35","unstructured":"Mitsos, A.: Man-Portable power generation devices: product design and supporting algorithms, http:\/\/yoric.mit.edu\/download\/Reports\/MitsosThesis.pdf . PhD thesis, Massachusetts Institute of Technology (2006)"},{"key":"9260_CR36","unstructured":"Mitsos, A., Barton, P.I.: Issues in the development of global optimization algorithms for bilevel programs with a nonconvex inner program. Technical Report, Massachusetts Institute of Technology (2006)"},{"key":"9260_CR37","unstructured":"Mitsos, A., Barton, P.I.: A test set for bilevel programs, http:\/\/yoric.mit.edu\/download\/Reports\/bileveltestset.pdf . Technical Report, Massachusetts Institute of Technology (2006)"},{"key":"9260_CR38","doi-asserted-by":"crossref","unstructured":"Mitsos, A., Lemonidis, P., Lee, C.K., Barton, P.I.: Relaxation-based bounds for semi-infinite programs. SIAM J. Optim. (SIOPT), Accepted for publication (2007)","DOI":"10.1137\/060674685"},{"issue":"5","key":"9260_CR39","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1287\/opre.38.5.911","volume":"38","author":"J.T. Moore","year":"1990","unstructured":"Moore J.T. and Bard J.F. (1990). The mixed integer linear bilevel programming problem. Oper. Res. 38(5): 911\u2013921","journal-title":"Oper. Res."},{"key":"9260_CR40","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970906","volume-title":"Methods and Applications of Interval Analysis","author":"R. Moore","year":"1979","unstructured":"Moore R. (1979). Methods and Applications of Interval Analysis. SIAM, Philadelphia, PA"},{"key":"9260_CR41","volume-title":"Integer and Combinatorial Optimization","author":"G.L. Nemhauser","year":"1999","unstructured":"Nemhauser G.L. and Wolsey L.A. (1999). Integer and Combinatorial Optimization. Wiley-Interscience, New York"},{"issue":"1\u20132","key":"9260_CR42","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1016\/j.combustflame.2006.02.009","volume":"146","author":"O.O. Oluwole","year":"2006","unstructured":"Oluwole O.O., Bhattacharjee B., Tolsma J.E., Barton P.I. and Green W.H. Jr. (2006). Rigorous valid ranges for optimally reduced kinetic models. Combust. Flame 146(1\u20132): 348\u2013365","journal-title":"Combust. Flame"},{"issue":"1","key":"9260_CR43","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/S0098-1354(98)00267-1","volume":"23","author":"K.H. Sahin","year":"1998","unstructured":"Sahin K.H. and Ciric A.R. (1998). A dual temperature simulated annealing approach for solving bilevel programming problems. Comput. Chem Eng. 23(1): 11\u201325","journal-title":"Comput. Chem Eng."},{"key":"9260_CR44","unstructured":"Sahinidis, N., Tawarmalani, M.: BARON. http:\/\/www.gams.com\/solvers\/baron.pdf (2005)"},{"key":"9260_CR45","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-6305-1","volume-title":"Nondifferentiable and Two-Level Mathematical Programming","author":"K. Shimizu","year":"1997","unstructured":"Shimizu K., Ishizuka Y. and Bard J.F. (1997). Nondifferentiable and Two-Level Mathematical Programming. Kluwer Academic Publishers, Boston"},{"issue":"10","key":"9260_CR46","doi-asserted-by":"crossref","first-page":"1951","DOI":"10.1016\/j.compchemeng.2004.03.011","volume":"28","author":"O. Stein","year":"2004","unstructured":"Stein O., Oldenburg J. and Marquardt W. (2004). Continuous reformulations of discrete-continuous optimization problems. Comput. Chem. Eng. 28(10): 1951\u20131966","journal-title":"Comput. Chem. Eng."},{"issue":"3","key":"9260_CR47","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1137\/S0363012901398393","volume":"42","author":"O. Stein","year":"2003","unstructured":"Stein O. and Still G. (2003). Solving semi-infinite optimization problems with interior point techniques. SIAM J. Control Optim. 42(3): 769\u2013788","journal-title":"SIAM J. Control Optim."},{"key":"9260_CR48","volume-title":"Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming. Nonconvex Optimization and its Applications","author":"M. Tawarmalani","year":"2002","unstructured":"Tawarmalani M. and Sahinidis N.V. (2002). Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming. Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Boston"},{"issue":"6","key":"9260_CR49","doi-asserted-by":"crossref","first-page":"1826","DOI":"10.1021\/ie990734o","volume":"39","author":"J. Tolsma","year":"2000","unstructured":"Tolsma J. and Barton P.I. (2000). DAEPACK: an open modeling environment for legacy models. Indust. Eng. Chem. Res. 39(6): 1826\u20131839","journal-title":"Indust. Eng. Chem. Res."},{"issue":"4","key":"9260_CR50","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s10898-006-9093-1","volume":"38","author":"H. Tuy","year":"2007","unstructured":"Tuy H., Migdalas A. and Hoai-Phuong N.T. (2007). A novel approach to bilevel nonlinear programming. J. Glob. Optim. 38(4): 527\u2013554","journal-title":"J. Glob. Optim."},{"issue":"1","key":"9260_CR51","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01100237","volume":"3","author":"H. Tuy","year":"1993","unstructured":"Tuy H., Migdalas A. and Varbrand P. (1993). A global optimization approach for the linear 2-level program. J. Glob. Optim. 3(1): 1\u201323","journal-title":"J. Glob. Optim."},{"issue":"3","key":"9260_CR52","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1007\/BF01098360","volume":"4","author":"H. Tuy","year":"1994","unstructured":"Tuy H., Migdalas A. and Varbrand P. (1994). A quasi-concave minimization method for solving linear 2-level programs. J. Glob. Optim. 4(3): 243\u2013263","journal-title":"J. Glob. Optim."},{"issue":"3","key":"9260_CR53","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/BF01096458","volume":"5","author":"L.N. Vicente","year":"1994","unstructured":"Vicente L.N. and Calamai P.H. (1994). Bilevel and multilevel programming \u2013 A bibliography review. J. Glob. Optim. 5(3): 291\u2013306","journal-title":"J. Glob. Optim."},{"key":"9260_CR54","volume-title":"Model Building in Mathematical Programming","author":"H.P. Williams","year":"1990","unstructured":"Williams H.P. (1990). Model Building in Mathematical Programming, 3rd edn. John Wiley and Sons, Chichester","edition":"3"},{"issue":"4","key":"9260_CR55","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1007\/BF01933221","volume":"30","author":"S. Zuhe","year":"1990","unstructured":"Zuhe S., Neumaier A. and Eiermann M.C. (1990). Solving minimax problems by interval-methods. BIT 30(4): 742\u2013751","journal-title":"BIT"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-007-9260-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-007-9260-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-007-9260-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T08:12:10Z","timestamp":1559290330000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-007-9260-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12,5]]},"references-count":55,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,12]]}},"alternative-id":["9260"],"URL":"https:\/\/doi.org\/10.1007\/s10898-007-9260-z","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,12,5]]}}}