{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T15:17:31Z","timestamp":1782314251652,"version":"3.54.5"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2011,2,24]],"date-time":"2011-02-24T00:00:00Z","timestamp":1298505600000},"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":[[2011,12]]},"DOI":"10.1007\/s10898-011-9664-7","type":"journal-article","created":{"date-parts":[[2011,2,23]],"date-time":"2011-02-23T10:30:25Z","timestamp":1298457025000},"page":"569-606","source":"Crossref","is-referenced-by-count":100,"title":["Generalized McCormick relaxations"],"prefix":"10.1007","volume":"51","author":[{"given":"Joseph K.","family":"Scott","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matthew D.","family":"Stuber","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":[[2011,2,24]]},"reference":[{"issue":"9","key":"9664_CR1","doi-asserted-by":"crossref","first-page":"1769","DOI":"10.1002\/aic.690460908","volume":"46","author":"C.S. Adjiman","year":"2000","unstructured":"Adjiman C.S., Androulakis I.P., Floudas C.A.: Global optimization of mixed-integer nonlinear problems. AIChE J. 46(9), 1769\u20131797 (2000)","journal-title":"AIChE J."},{"key":"9664_CR2","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/BF01099647","volume":"7","author":"I.P. Androulakis","year":"1995","unstructured":"Androulakis I.P., Maranas C.D., Floudas C.A.: \u03b1BB: a global optimization method for general constrained nonconvex problems. J. Glob. Optim. 7, 337\u2013363 (1995)","journal-title":"J. Glob. Optim."},{"key":"9664_CR3","unstructured":"Chachuat, B.: libMC: A numeric library for McCormick relaxation of factorable functions. Documentation and Source Code available at: http:\/\/yoric.mit.edu\/libMC\/ (2007)"},{"issue":"3","key":"9664_CR4","doi-asserted-by":"crossref","first-page":"274","DOI":"10.2478\/s11696-009-0017-7","volume":"63","author":"M. Cizniar","year":"2009","unstructured":"Cizniar M., Podmajersky M., Hirmajer T., Fikar M., Latifi A.M.: Global optimization for parameter estimation of differential-algebraic systems. Chem. Pap. 63(3), 274\u2013283 (2009)","journal-title":"Chem. Pap."},{"issue":"2","key":"9664_CR5","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1063\/1.4822377","volume":"10","author":"S.D. Cohen","year":"1996","unstructured":"Cohen S.D., Hindmarsh A.C.: CVODE, a stiff\/nonstiff ODE solver in C. Comput. Phys. 10(2), 138\u2013143 (1996)","journal-title":"Comput. Phys."},{"issue":"8","key":"9664_CR6","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1002\/aic.690330804","volume":"33","author":"J.E. Cuthrell","year":"1987","unstructured":"Cuthrell J.E., Biegler L.T.: On the optimization of differential-algebraic process systems. AIChE J. 33(8), 1257\u20131270 (1987)","journal-title":"AIChE J."},{"key":"9664_CR7","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1023\/A:1026578104213","volume":"17","author":"W.R. Esposito","year":"2000","unstructured":"Esposito W.R., Floudas C.A.: Deterministic global optimization in nonlinear optimal control problems. J. Glob. Optim. 17, 97\u2013126 (2000)","journal-title":"J. Glob. Optim."},{"key":"9664_CR8","doi-asserted-by":"crossref","first-page":"1291","DOI":"10.1021\/ie990486w","volume":"39","author":"W.R. Esposito","year":"2000","unstructured":"Esposito W.R., Floudas C.A.: Global optimization for the parameter estimation of differential-algebraic systems. Ind. Eng. Chem. Res. 39, 1291\u20131310 (2000)","journal-title":"Ind. Eng. Chem. Res."},{"issue":"4","key":"9664_CR9","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1137\/0718043","volume":"18","author":"D.M. Gay","year":"1981","unstructured":"Gay D.M.: Perturbation bounds for nonlinear equations. SIAM J. Numer. Anal. 18(4), 654\u2013663 (1981)","journal-title":"SIAM J. Numer. Anal."},{"key":"9664_CR10","unstructured":"Harrison, G.W.: Dynamic models with uncertain parameters. In: Avula, X. (ed.) Proceedings of the First International Conference on Mathematical Modeling, vol. 1, pp. 295\u2013304. (1977)"},{"key":"9664_CR11","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., Tuy H.: Global Optimization: deterministic approaches, 3rd edn. Springer, New York (1996)","edition":"3"},{"key":"9664_CR12","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., Barton P.I.: Outer approximation algorithms for separable nonconvex mixed-integer nonlinear programs. Math. Program. 100, 517\u2013535 (2004)","journal-title":"Math. Program."},{"key":"9664_CR13","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1023\/A:1021924706467","volume":"25","author":"L. Liberti","year":"2003","unstructured":"Liberti L., Pantelides C.C.: Convex envelopes of monomials of odd degree. J. Glob. Optim. 25, 157\u2013168 (2003)","journal-title":"J. Glob. Optim."},{"key":"9664_CR14","doi-asserted-by":"crossref","first-page":"1714","DOI":"10.1016\/j.compchemeng.2007.08.013","volume":"32","author":"Y. Lin","year":"2008","unstructured":"Lin Y., Enszer J.A., Stadtherr M.A.: Enclosing all solutions of two-point boundary value problems for ODEs. Comput. Chem. Eng. 32, 1714\u20131725 (2008)","journal-title":"Comput. Chem. Eng."},{"key":"9664_CR15","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1016\/j.apnum.2006.10.006","volume":"57","author":"Y. Lin","year":"2007","unstructured":"Lin Y., Stadtherr M.A.: Validated solutions of initial value problems for parametric ODEs. Appl. Numer. Math. 57, 1145\u20131162 (2007)","journal-title":"Appl. Numer. Math."},{"key":"9664_CR16","doi-asserted-by":"crossref","first-page":"780","DOI":"10.1002\/cjce.5450700423","volume":"70","author":"R. Luus","year":"1992","unstructured":"Luus R., Dittrich J., Keil F.J.: Multiplicity of solutions in the optimization of a bifunctional catalyst blend in a tubular reactor. Can. J. Chem. Eng. 70, 780\u2013785 (1992)","journal-title":"Can. J. Chem. Eng."},{"key":"9664_CR17","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF01580665","volume":"10","author":"G.P. McCormick","year":"1976","unstructured":"McCormick G.P.: Computability of global solutions to factorable nonconvex programs: Part I - convex underestimating problems. Math. Program. 10, 147\u2013175 (1976)","journal-title":"Math. Program."},{"issue":"2","key":"9664_CR18","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1137\/080717341","volume":"20","author":"A. Mitsos","year":"2009","unstructured":"Mitsos A., Chachuat B., Barton P.I.: McCormick-based relaxations of algorithms. SIAM J. Optim. 20(2), 573\u2013601 (2009)","journal-title":"SIAM J. Optim."},{"issue":"8","key":"9664_CR19","doi-asserted-by":"crossref","first-page":"2251","DOI":"10.1002\/aic.690420814","volume":"42","author":"M.J. Mohideen","year":"1996","unstructured":"Mohideen M.J., Perkins J.D., Pistikopoulos E.N.: Optimal design of dynamic systems under uncertainty. AIChE J. 42(8), 2251\u20132272 (1996)","journal-title":"AIChE J."},{"key":"9664_CR20","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970906","volume-title":"Methods and Applications of Interval Analysis","author":"R.E. Moore","year":"1979","unstructured":"Moore R.E.: Methods and Applications of Interval Analysis. SIAM, Philidelphia, PA (1979)"},{"key":"9664_CR21","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0096-3003(98)10083-8","volume":"105","author":"N.S. Nedialkov","year":"1999","unstructured":"Nedialkov N.S., Jackson K.R., Corliss G.F.: Validated solutions of initial value problems for ordinary differential equations. Appl. Math. Comput. 105, 21\u201368 (1999)","journal-title":"Appl. Math. Comput."},{"key":"9664_CR22","volume-title":"Interval Methods for Systems of Equations","author":"A. Neumaier","year":"1990","unstructured":"Neumaier A.: Interval Methods for Systems of Equations. Cambridge University Press, Cambridge (1990)"},{"issue":"1","key":"9664_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1016259507911","volume":"24","author":"I. Papamichail","year":"2002","unstructured":"Papamichail I., Adjiman C.S.: A rigorous global optimization algorithm for problems with ordinary differential equations. J. Glob. Optim. 24(1), 1\u201333 (2002)","journal-title":"J. Glob. Optim."},{"key":"9664_CR24","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/s10898-004-6100-2","volume":"33","author":"I. Papamichail","year":"2005","unstructured":"Papamichail I., Adjiman C.S.: Proof of convergence for a global optimization algorithms for problems with ordinary differential equations. J. Glob. Optim. 33, 83\u2013107 (2005)","journal-title":"J. Glob. Optim."},{"key":"9664_CR25","volume-title":"Principles of Mathematical Analysis","author":"W. Rudin","year":"1964","unstructured":"Rudin W.: Principles of Mathematical Analysis, 3rd edn. McGraw-Hill, New York (1964)","edition":"3"},{"key":"9664_CR26","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1016\/j.compchemeng.2009.11.021","volume":"34","author":"J.K. Scott","year":"2010","unstructured":"Scott J.K., Barton P.I.: Tight, efficient bounds on the solutions of chemical kinetics models. Comput. Chem. Eng. 34, 717\u2013731 (2010)","journal-title":"Comput. Chem. Eng."},{"key":"9664_CR27","unstructured":"Scott, J.K., Chachuat, B., Barton, P.I.: Nonlinear Convex and Concave Relaxations for the Solutions of Parametric ODEs. (2009, submitted)"},{"key":"9664_CR28","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1023\/B:JOTA.0000037606.79050.a7","volume":"121","author":"A.B. Singer","year":"2004","unstructured":"Singer A.B., Barton P.I.: Global solution of optimization problems with parameter-embedded linear dynamic systems. J. Optim. Theory Appl. 121, 613\u2013646 (2004)","journal-title":"J. Optim. Theory Appl."},{"key":"9664_CR29","doi-asserted-by":"crossref","first-page":"2167","DOI":"10.1137\/040604388","volume":"27","author":"A.B. Singer","year":"2006","unstructured":"Singer A.B., Barton P.I.: Bounding the solutions of parameter dependent nonlinear ordinary differential equations. SIAM J. Sci. Comput. 27, 2167\u20132182 (2006)","journal-title":"SIAM J. Sci. Comput."},{"key":"9664_CR30","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10898-005-7074-4","volume":"34","author":"A.B. Singer","year":"2006","unstructured":"Singer A.B., Barton P.I.: Global optimization with nonlinear ordinary differential equations. J. Glob. Optim. 34, 159\u2013190 (2006)","journal-title":"J. Glob. Optim."},{"key":"9664_CR31","unstructured":"Stuber, M.D., Barton, P.I.: On parametric interval Newton methods. (2009, in preparation)"},{"key":"9664_CR32","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3532-1","volume-title":"Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming","author":"M. Tawarmalani","year":"2002","unstructured":"Tawarmalani M., Sahinidis N.V.: Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming. Kluwer, Dordrecht (2002)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-011-9664-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-011-9664-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-011-9664-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T04:58:57Z","timestamp":1559278737000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-011-9664-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2,24]]},"references-count":32,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,12]]}},"alternative-id":["9664"],"URL":"https:\/\/doi.org\/10.1007\/s10898-011-9664-7","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2,24]]}}}