{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T07:27:07Z","timestamp":1761895627701},"reference-count":76,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,2,19]],"date-time":"2013-02-19T00:00:00Z","timestamp":1361232000000},"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":[[2014,2]]},"DOI":"10.1007\/s10898-013-0039-0","type":"journal-article","created":{"date-parts":[[2013,2,19]],"date-time":"2013-02-19T05:57:42Z","timestamp":1361253462000},"page":"207-242","source":"Crossref","is-referenced-by-count":11,"title":["Augmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming"],"prefix":"10.1007","volume":"58","author":[{"given":"E. G.","family":"Birgin","sequence":"first","affiliation":[]},{"given":"J. M.","family":"Mart\u00ednez","sequence":"additional","affiliation":[]},{"given":"L. F.","family":"Prudente","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,2,19]]},"reference":[{"key":"39_CR1","doi-asserted-by":"crossref","first-page":"S419","DOI":"10.1016\/0098-1354(96)00080-4","volume":"20","author":"CS Adjiman","year":"1996","unstructured":"Adjiman, C.S., Androulakis, I.P., Maranas, C.D., Floudas, C.A.: A global optimization method $\\alpha $BB for process design. Comput. Chem. Eng. 20, S419\u2013424 (1996)","journal-title":"Comput. Chem. Eng."},{"key":"39_CR2","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1016\/S0098-1354(98)00027-1","volume":"22","author":"CS Adjiman","year":"1998","unstructured":"Adjiman, C.S., Dallwig, S., Floudas, C.A., Neumaier, A.: A global optimization method, $\\alpha $BB, for general twice-differentiable constrained NLPs\u2014I. Theor. Adv. Comput. Chem. Eng. 22, 1137\u20131158 (1998)","journal-title":"Theor. Adv. Comput. Chem. Eng."},{"key":"39_CR3","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1016\/S0098-1354(98)00218-X","volume":"22","author":"CS Adjiman","year":"1998","unstructured":"Adjiman, C.S., Androulakis, I.P., Floudas, C.A.: A global optimization method, $\\alpha $BB, for general twice-differentiable constrained NLPs\u2014II. Implementation and computational results. Comput. Chem. Eng. 22, 1159\u20131179 (1998)","journal-title":"Comput. Chem. Eng."},{"key":"39_CR4","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1137\/S105262349935178X","volume":"10","author":"FA Al-Khayyal","year":"2000","unstructured":"Al-Khayyal, F.A., Sherali, H.D.: On finitely terminating Branch-and-Bound algorithms for some global optimization problems. SIAM J. Optim. 10, 1049\u20131057 (2000)","journal-title":"SIAM J. Optim."},{"key":"39_CR5","doi-asserted-by":"crossref","first-page":"1286","DOI":"10.1137\/060654797","volume":"18","author":"R Andreani","year":"2007","unstructured":"Andreani, R., Birgin, E.G., Mart\u00ednez, J.M., Schuverdt, M.L.: On augmented Lagrangian methods with general lower-level constraints. SIAM J. Optim. 18, 1286\u20131309 (2007)","journal-title":"SIAM J. Optim."},{"key":"39_CR6","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10107-006-0077-1","volume":"111","author":"R Andreani","year":"2008","unstructured":"Andreani, R., Birgin, E.G., Mart\u00ednez, J.M., Schuverdt, M.L.: Augmented Lagrangian methods under the constant positive linear dependence constraint qualification. Math. Program. 111, 5\u201332 (2008)","journal-title":"Math. Program."},{"key":"39_CR7","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s10589-009-9240-y","volume":"45","author":"R Andreani","year":"2010","unstructured":"Andreani, R., Birgin, E.G., Mart\u00ednez, J.M., Schuverdt, M.L.: Second-order negative-curvature methods for box-constrained and general constrained optimization. Comput. Optim. Appl. 45, 209\u2013236 (2010)","journal-title":"Comput. Optim. Appl."},{"key":"39_CR8","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1080\/02331930903578700","volume":"60","author":"R Andreani","year":"2011","unstructured":"Andreani, R., Haeser, G., Mart\u00ednez, J.M.: On sequential optimality conditions for smooth constrained optimization. Optimization 60, 627\u2013641 (2011)","journal-title":"Optimization"},{"key":"39_CR9","unstructured":"Andreani, R., Haeser, G., Schuverdt, M.L., Silva, P.J.S.: A relaxed constant positive linear dependence constraint qualification and applications. Math. Program. (to appear)"},{"key":"39_CR10","unstructured":"Andreani, R., Haeser, G., Schuverdt, M.L., Silva, P.J.S.: Two new weak constraint qualifications and applications. SIAM J. Optim. (to appear)"},{"key":"39_CR11","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/s10957-004-1861-9","volume":"125","author":"R Andreani","year":"2005","unstructured":"Andreani, R., Mart\u00ednez, J.M., Schuverdt, M.L.: On the relation between the constant positive linear dependence condition and quasinormality constraint qualification. J. Optim. Theory Appl. 125, 473\u2013485 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"39_CR12","doi-asserted-by":"crossref","first-page":"3533","DOI":"10.1137\/090777189","volume":"20","author":"R Andreani","year":"2010","unstructured":"Andreani, R., Mart\u00ednez, J.M., Svaiter, B.F.: A new sequential optimality condition for constrained optimization and algorithmic consequences. SIAM J. Optim. 20, 3533\u20133554 (2010)","journal-title":"SIAM J. Optim."},{"key":"39_CR13","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s11075-009-9289-9","volume":"53","author":"M Andretta","year":"2010","unstructured":"Andretta, M., Birgin, E.G., Mart\u00ednez, J.M.: Partial spectral projected gradient method with active-set strategy for linearly constrained optimization. Numer. Algorithms 53, 23\u201352 (2010)","journal-title":"Numer. Algorithms"},{"key":"39_CR14","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/BF01099647","volume":"7","author":"IP Androulakis","year":"1995","unstructured":"Androulakis, I.P., Maranas, C.D., Floudas, C.A.: $\\alpha $BB: a global optimization method for general constrained nonconvex problems. J. Glob. Optim. 7, 337\u2013363 (1995)","journal-title":"J. Glob. Optim."},{"key":"39_CR15","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1137\/070692662","volume":"20","author":"C Audet","year":"2009","unstructured":"Audet, C., Dennis Jr, J.E.: A progressive barrier for derivative-free nonlinear programming. SIAM J. Optim. 20, 445\u2013472 (2009)","journal-title":"SIAM J. Optim."},{"key":"39_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2836-1","volume-title":"Practical Bilevel Optimization. Algorithms and Applications. Kluwer Book Series: Nonconvex Optimization and its Applications","author":"JF Bard","year":"1998","unstructured":"Bard, J.F.: Practical Bilevel Optimization. Algorithms and Applications. Kluwer Book Series: Nonconvex Optimization and its Applications. Kluwer, Dordrecht, The Netherlands (1998)"},{"key":"39_CR17","doi-asserted-by":"crossref","unstructured":"Birgin, E.G., Bustamante, L.H., Callisaya, H.F., Mart\u00ednez, J.M.: Packing circles within ellipses. Int. Trans. Oper. Res. doi: 10.1111\/itor.12006","DOI":"10.1111\/itor.12006"},{"key":"39_CR18","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1007\/s10957-011-9815-5","volume":"150","author":"EG Birgin","year":"2011","unstructured":"Birgin, E.G., Castelani, E.V., Martinez, A.L., Mart\u00ednez, J.M.: Outer trust-region method for constrained optimization. J. Optim. Theory Appl. 150, 142\u2013155 (2011)","journal-title":"J. Optim. Theory Appl."},{"key":"39_CR19","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10589-005-1066-7","volume":"31","author":"EG Birgin","year":"2005","unstructured":"Birgin, E.G., Castillo, R., Mart\u00ednez, J.M.: Numerical comparison of augmented Lagrangian algorithms for nonconvex problems. Comput. Optim. Appl. 31, 31\u201356 (2005)","journal-title":"Comput. Optim. Appl."},{"key":"39_CR20","doi-asserted-by":"crossref","unstructured":"Birgin, E.G., Fern\u00e1ndez, D., Mart\u00ednez, J.M.: On the boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems. Optim. Methods Softw. doi: 10.1080\/10556788.2011.556634","DOI":"10.1080\/10556788.2011.556634"},{"key":"39_CR21","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s10107-009-0264-y","volume":"125","author":"EG Birgin","year":"2010","unstructured":"Birgin, E.G., Floudas, C.A., Mart\u00ednez, J.M.: Global minimization using an augmented Lagrangian method with variable lower-level constraints. Math. Program. 125, 139\u2013162 (2010)","journal-title":"Math. Program."},{"key":"39_CR22","unstructured":"Birgin, E.G., Floudas, C.A., Mart\u00ednez, J.M.: Global Minimization Using an Augmented Lagrangian Method with Variable Lower-level Constraints. Technical Report MCDO220107. Department of Applied Mathematics, Unicamp, Brazil (2007) (see http:\/\/www.ime.usp.br\/~egbirgin\/ )"},{"key":"39_CR23","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1023\/A:1019928808826","volume":"23","author":"EG Birgin","year":"2002","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Large-scale active-set box-constrained optimization method with spectral projected gradients. Comput. Optim. Appl. 23, 101\u2013125 (2002)","journal-title":"Comput. Optim. Appl."},{"key":"39_CR24","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1080\/10556780701577730","volume":"23","author":"EG Birgin","year":"2008","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Improving ultimate convergence of an augmented Lagrangian method. Optim. Methods Softw. 23, 177\u2013195 (2008)","journal-title":"Optim. Methods Softw."},{"key":"39_CR25","doi-asserted-by":"crossref","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Practical augmented Lagrangian methods. In: Floudas, C.A., Pardalos, P.M. (eds.) Encyclopedia of Optimization, 2nd edn, pp. 3013\u20133023. Springer, Berlin (2009)","DOI":"10.1007\/978-0-387-74759-0_517"},{"key":"39_CR26","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1007\/s10589-011-9396-0","volume":"51","author":"EG Birgin","year":"2012","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization. Comput. Optim. Appl. 51, 941\u2013965 (2012)","journal-title":"Comput. Optim. Appl."},{"key":"39_CR27","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Prudente, L.: Global Nonlinear Programming with Possible Infeasibility and Finite Termination. Technical Report MCDO250612. Department of Applied Mathematics, Unicamp, Brazil (2012) (see http:\/\/www.ime.usp.br\/~egbirgin\/ )"},{"key":"39_CR28","unstructured":"Callisaya, H.F.: Empacotamento em quadr\u00e1ticas. PhD Thesis, Institute of Mathematics, Statistics and Scientific Computing, University of Campinas (2012)"},{"key":"39_CR29","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s10589-009-9271-4","volume":"46","author":"EV Castelani","year":"2010","unstructured":"Castelani, E.V., Martinez, A.L., Mart\u00ednez, J.M., Svaiter, B.F.: Addressing the greediness phenomenon in nonlinear programming by means of proximal augmented Lagrangians. Comput. Optim. Appl. 46, 229\u2013245 (2010)","journal-title":"Comput. Optim. Appl."},{"key":"39_CR30","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719857","volume-title":"Trust Region Methods. MPS\/SIAM Series on Optimization","author":"AR Conn","year":"2000","unstructured":"Conn, A.R., Gould, N.I.M., Toint, PhL: Trust Region Methods. MPS\/SIAM Series on Optimization. SIAM, Philadelphia (2000)"},{"key":"39_CR31","first-page":"19","volume":"30","author":"MA Diniz-Ehrhardt","year":"2011","unstructured":"Diniz-Ehrhardt, M.A., Mart\u00ednez, J.M., Pedroso, L.G.: Derivative-free methods for nonlinear programming with general lower-level constraints. Comput. Appl. Math. 30, 19\u201352 (2011)","journal-title":"Comput. Appl. Math."},{"key":"39_CR32","volume-title":"Optimal Quadratic Programming Algorithms","author":"Z Dost\u00e1l","year":"2009","unstructured":"Dost\u00e1l, Z.: Optimal Quadratic Programming Algorithms. Springer, New York (2009)"},{"key":"39_CR33","doi-asserted-by":"crossref","first-page":"1120","DOI":"10.1137\/S1052623499362573","volume":"13","author":"Z Dost\u00e1l","year":"2003","unstructured":"Dost\u00e1l, Z., Friedlander, A., Santos, S.A.: Augmented Lagrangians with adaptive precision control for quadratic programming with simple bounds and equality constraints. SIAM J. Optim. 13, 1120\u20131140 (2003)","journal-title":"SIAM J. Optim."},{"key":"39_CR34","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s10107-003-0374-x","volume":"96","author":"J Eckstein","year":"2003","unstructured":"Eckstein, J.: A practical general approximation criterion for methods of multipliers based on Bregman distances. Math. Program. 96, 61\u201386 (2003)","journal-title":"Math. Program."},{"key":"39_CR35","volume-title":"Deterministic Global Optimization: Theory, Methods and Application","author":"CA Floudas","year":"1999","unstructured":"Floudas, C.A.: Deterministic Global Optimization: Theory, Methods and Application. Kluwer, DorDrecht, Boston, London (1999)"},{"key":"39_CR36","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1016\/j.compchemeng.2005.02.006","volume":"29","author":"CA Floudas","year":"2005","unstructured":"Floudas, C.A., Akrotirianakis, I.G., Caratzoulas, S., Meyer, C.A., Kallrath, J.: Global optimization in the 21st century: advances and challenges. Comput. Chem. Eng. 29, 1185\u20131202 (2005)","journal-title":"Comput. Chem. Eng."},{"key":"39_CR37","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10898-008-9332-8","volume":"45","author":"CA Floudas","year":"2009","unstructured":"Floudas, C.A., Gounaris, C.E.: A review of recent advances in global optimization. J. Glob. Optim. 45, 3\u201338 (2009)","journal-title":"J. Glob. Optim."},{"key":"39_CR38","doi-asserted-by":"crossref","first-page":"1397","DOI":"10.1016\/0098-1354(90)80020-C","volume":"14","author":"CA Floudas","year":"1990","unstructured":"Floudas, C.A., Visweeswaran, V.: A global optimization algorithm (GOP) for certain classes of nonconvex NLPs\u2014I. Theory Comput. Chem. Eng. 14, 1397\u20131417 (1990)","journal-title":"Theory Comput. Chem. Eng."},{"key":"39_CR39","doi-asserted-by":"crossref","unstructured":"Gao, D.Y.: Duality Principles in Nonconvex Systems: Theory, Methods, and Applications. Kluwer, Dordrecht, The Netherlands (1999)","DOI":"10.1007\/978-1-4757-3176-7_3"},{"key":"39_CR40","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1023\/A:1026537630859","volume":"17","author":"DY Gao","year":"2000","unstructured":"Gao, D.Y.: Canonical dual transformation method and generalized triality theory in nonsmooth global optimization. J. Glob. Optim. 17, 127\u2013160 (2000)","journal-title":"J. Glob. Optim."},{"key":"39_CR41","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1080\/02331930310001611501","volume":"52","author":"DY Gao","year":"2003","unstructured":"Gao, D.Y.: Perfect duality theory and complete solutions to a class of global optimization problems, generalized triality theory in nonsmooth global optimization. Optimization 52, 467\u2013493 (2003)","journal-title":"Optimization"},{"key":"39_CR42","unstructured":"Gao, D.Y.: Canonical duality theory and solutions to constrained nonconvex quadratic programming. J. Glob. Optim. 29, 337\u2013399 (2004)"},{"key":"39_CR43","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s10898-005-3068-5","volume":"35","author":"DY Gao","year":"2006","unstructured":"Gao, D.Y.: Complete solutions and extremality criteria to polynomial optimization problems. J. Glob. Optim. 35, 131\u2013143 (2006)","journal-title":"J. Glob. Optim."},{"key":"39_CR44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3934\/jimo.2007.3.1","volume":"3","author":"DY Gao","year":"2007","unstructured":"Gao, D.Y.: Solutions and optimality to box constrained nonconvex minimization problems. J. Ind. Manag. Optim. 3, 1\u201312 (2007)","journal-title":"J. Ind. Manag. Optim."},{"key":"39_CR45","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1007\/BF00940552","volume":"79","author":"WW Hager","year":"1993","unstructured":"Hager, W.W.: Analysis and implementation of a dual algorithm for constrained optimization. J. Optim. Theory Appl. 79, 427\u2013462 (1993)","journal-title":"J. Optim. Theory Appl."},{"key":"39_CR46","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF00927673","volume":"4","author":"MR Hestenes","year":"1969","unstructured":"Hestenes, M.R.: Multiplier and gradient methods. J. Optim. Theory Appl. 4, 303\u2013320 (1969)","journal-title":"J. Optim. Theory Appl."},{"key":"39_CR47","doi-asserted-by":"crossref","unstructured":"Horst, R., Pardalos, P.M., Thoai, M.V.: Introduction to Global Optimization. Kluwer Book Series: Nonconvex Optimization and its Applications. Kluwer, Dordrecht, The Netherlands (2000)","DOI":"10.1007\/978-1-4615-0015-5"},{"key":"39_CR48","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1145\/198429.198433","volume":"20","author":"RB Kearfott","year":"1994","unstructured":"Kearfott, R.B., Dawande, M., Du, K., Hu, C.: Algorithm 737: INTLIB: a portable Fortran 77 interval standard-function library. ACM Trans. Math. Softw. 20, 447\u2013459 (1994)","journal-title":"ACM Trans. Math. Softw."},{"key":"39_CR49","unstructured":"Lewis, R.M., Torczon, V.: A Direct Search Approach to Nonlinear Programming Problems Using an Augmented Lagrangian Method with Explicit Treatment of Linear Constraints. Technical Report WM-CS-2010-01. College of William & Mary, Department of Computer Sciences (2010)"},{"key":"39_CR50","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1111\/j.1475-3995.2004.00438.x","volume":"11","author":"L Liberti","year":"2004","unstructured":"Liberti, L.: Reduction constraints for the global optimization of NLPs. Int. Trans. Oper. Res. 11, 33\u201341 (2004)","journal-title":"Int. Trans. Oper. Res."},{"key":"39_CR51","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/0-387-30528-9_8","volume-title":"Global Optimization: From Theory to Implementation","author":"L Liberti","year":"2006","unstructured":"Liberti, L.: Writing global optimization software. In: Liberti, L., Maculan, N. (eds.) Global Optimization: From Theory to Implementation, pp. 211\u2013262. Springer, Berlin (2006)"},{"key":"39_CR52","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s10898-006-9005-4","volume":"36","author":"L Liberti","year":"2006","unstructured":"Liberti, L., Pantelides, C.C.: An exact reformulation algorithm for large nonconvex NLPs involving bilinear terms. J. Glob. Optim. 36, 161\u2013189 (2006)","journal-title":"J. Glob. Optim."},{"key":"39_CR53","first-page":"1209","volume":"18","author":"HZ Luo","year":"2007","unstructured":"Luo, H.Z., Sun, X.L., Li, D.: On the convergence of augmented Lagrangian methods for constrained global optimization. SIAM J. Optim. 18, 1209\u20131230 (2007)","journal-title":"SIAM J. Optim."},{"key":"39_CR54","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s11075-012-9561-2","volume":"60","author":"JM Mart\u00ednez","year":"2012","unstructured":"Mart\u00ednez, J.M., Prudente, L.F.: Handling infeasibility in a large-scale nonlinear optimization algorithm. Numer. Algorithms 60, 263\u2013277 (2012)","journal-title":"Numer. Algorithms"},{"key":"39_CR55","unstructured":"Murtagh, B.A., Saunders, M.A.: MINOS 5.4 User\u2019s Guide. System Optimization Laboratory, Department of Operations Research, Standford University, CA (1993)"},{"key":"39_CR56","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1017\/S0962492904000194","volume":"13","author":"A Neumaier","year":"2004","unstructured":"Neumaier, A.: Complete search in continuous global optimization and constraints satisfaction. Acta Numer. 13, 271\u2013369 (2004)","journal-title":"Acta Numer."},{"key":"39_CR57","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s10107-005-0585-4","volume":"103","author":"A Neumaier","year":"2005","unstructured":"Neumaier, A., Shcherbina, O., Huyer, W., Vink\u00f3, T.: A comparison of complete global optimization solvers. Math. Program. 103, 335\u2013356 (2005)","journal-title":"Math. Program."},{"key":"39_CR58","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1080\/10556780108805820","volume":"15","author":"G Pacelli","year":"2001","unstructured":"Pacelli, G., Recchioni, M.C.: An interior point algorithm for global optimal solutions and KKT points. Optim. Methods Softw 15, 225\u2013256 (2001)","journal-title":"Optim. Methods Softw"},{"key":"39_CR59","unstructured":"Powell, M.J.D.: A method for nonlinear constraints in minimization problems. In: Fletcher, R. (ed.) Optimization, pp. 283\u2013298. Academic Press, New York, NY (1969)"},{"key":"39_CR60","volume-title":"Numerical Recipes in Fortran: The Art of Scientific Computing","author":"WH Press","year":"1992","unstructured":"Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in Fortran: The Art of Scientific Computing. Cambridge University Press, New York (1992)"},{"key":"39_CR61","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1137\/0312021","volume":"12","author":"RT Rockafellar","year":"1974","unstructured":"Rockafellar, R.T.: Augmented Lagrange multiplier functions and duality in nonconvex programming. SIAM J. Control Optim. 12, 268\u2013285 (1974)","journal-title":"SIAM J. Control Optim."},{"key":"39_CR62","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/BF00138689","volume":"8","author":"HS Ryoo","year":"1996","unstructured":"Ryoo, H.S., Sahinidis, N.V.: A branch-and-reduce approach to global optimization. J. Glob. Optim. 8, 107\u2013138 (1996)","journal-title":"J. Glob. Optim."},{"key":"39_CR63","unstructured":"Sahinidis, N.V., Tawarmalani, M.: BARON 9.0.4: Global Optimization of Mixed-Integer Nonlinear Programs, User\u2019s manual (2010)"},{"key":"39_CR64","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4388-3","volume-title":"A Reformulation-linearization Technique for Solving Discrete and Continuous Nonconvex Problems. Kluwer Book Series: Nonconvex Optimization and its Applications","author":"HD Sherali","year":"1999","unstructured":"Sherali, H.D., Adams, W.P.: A Reformulation-linearization Technique for Solving Discrete and Continuous Nonconvex Problems. Kluwer Book Series: Nonconvex Optimization and its Applications. Kluwer, Dordrecht, The Netherlands (1999)"},{"key":"39_CR65","first-page":"197","volume":"14","author":"HD Sherali","year":"1995","unstructured":"Sherali, H.D., Alameddine, A., Glickman, T.S.: Biconvex models and algorithms for risk management problems. Am. J. Math. Manag. Sci. 14, 197\u2013228 (1995)","journal-title":"Am. J. Math. Manag. Sci."},{"key":"39_CR66","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s10898-004-2706-7","volume":"32","author":"HD Sherali","year":"2005","unstructured":"Sherali, H.D., Desai, J.: A global optimization RLT-based approach for solving the hard clustering problem. J. Glob. Optim. 32, 281\u2013306 (2005)","journal-title":"J. Glob. Optim."},{"key":"39_CR67","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s10898-004-7390-0","volume":"33","author":"HD Sherali","year":"2005","unstructured":"Sherali, H.D., Desai, J.: A global optimization RLT-based approach for solving the fuzzy clustering problem. J. Glob. Optim. 33, 597\u2013615 (2005)","journal-title":"J. Glob. Optim."},{"key":"39_CR68","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/BF00121304","volume":"2","author":"HD Sherali","year":"1992","unstructured":"Sherali, H.D., Tuncbilek, C.H.: A global optimization algorithm for polynomial programming problems using a reformulation-linearization technique. J. Glob. Optim. 2, 101\u2013112 (1992)","journal-title":"J. Glob. Optim."},{"key":"39_CR69","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0167-6377(97)00013-8","volume":"21","author":"HD Sherali","year":"1997","unstructured":"Sherali, H.D., Tuncbilek, C.H.: New reformulation-linearization\/convexification relaxations for univariate and multivariate polynomial programming problems. Oper. Res. Lett. 21, 1\u201310 (1997)","journal-title":"Oper. Res. Lett."},{"key":"39_CR70","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/PL00011409","volume":"89","author":"HD Sherali","year":"2001","unstructured":"Sherali, H.D., Wang, H.: Global optimization of nonconvex factorable programming problems. Math. Program. 89, 459\u2013478 (2001)","journal-title":"Math. Program."},{"key":"39_CR71","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/S0098-1354(98)00286-5","volume":"23","author":"EMB Smith","year":"1999","unstructured":"Smith, E.M.B., Pantelides, C.C.: A symbolic reformulation\/spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs. Comput. Chem. Eng. 23, 457\u2013478 (1999)","journal-title":"Comput. Chem. Eng."},{"key":"39_CR72","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. Kluwer Book Series: Nonconvex Optimization and its Applications","author":"M Tawarmalani","year":"2002","unstructured":"Tawarmalani, M., Sahinidis, N.V.: Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming. Kluwer Book Series: Nonconvex Optimization and its Applications. Kluwer, Dordrecht, The Netherlands (2002)"},{"key":"39_CR73","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s10107-005-0581-8","volume":"103","author":"M Tawarmalani","year":"2005","unstructured":"Tawarmalani, M., Sahinidis, N.V.: A polyhedral branch-and-cut approach to global optimization. Math. Program. 103, 225\u2013249 (2005)","journal-title":"Math. Program."},{"key":"39_CR74","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2809-5","volume-title":"Convex Analysis and Global Optimization. Kluwer Book Series: Nonconvex Optimization and its Applications","author":"H Tuy","year":"1998","unstructured":"Tuy, H.: Convex Analysis and Global Optimization. Kluwer Book Series: Nonconvex Optimization and its Applications. Kluwer, Dordrecht, The Netherlands (1998)"},{"key":"39_CR75","doi-asserted-by":"crossref","first-page":"1419","DOI":"10.1016\/0098-1354(90)80021-3","volume":"14","author":"V Visweeswaran","year":"1990","unstructured":"Visweeswaran, V., Floudas, C.A.: A global optimization algorithm (GOP) for certain classes of nonconvex NLPs\u2014II. Application of theory and test problems. Comput. Chem. Eng. 14, 1419\u20131434 (1990)","journal-title":"Comput. Chem. Eng."},{"key":"39_CR76","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9182-9","volume-title":"Stochastic Adaptive Search for Global Optimization. Kluwer Book Series: Nonconvex Optimization and its Applications","author":"ZB Zabinsky","year":"2003","unstructured":"Zabinsky, Z.B.: Stochastic Adaptive Search for Global Optimization. Kluwer Book Series: Nonconvex Optimization and its Applications. Kluwer, Dordrecht, The Netherlands (2003)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-013-0039-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-013-0039-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-013-0039-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T21:45:21Z","timestamp":1562708721000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-013-0039-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,19]]},"references-count":76,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,2]]}},"alternative-id":["39"],"URL":"https:\/\/doi.org\/10.1007\/s10898-013-0039-0","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2,19]]}}}