{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T17:25:18Z","timestamp":1778347518810,"version":"3.51.4"},"reference-count":76,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[1996,3,1]],"date-time":"1996-03-01T00:00:00Z","timestamp":825638400000},"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":[[1996,3]]},"DOI":"10.1007\/bf00138689","type":"journal-article","created":{"date-parts":[[2004,11,3]],"date-time":"2004-11-03T16:09:59Z","timestamp":1099498199000},"page":"107-138","source":"Crossref","is-referenced-by-count":260,"title":["A branch-and-reduce approach to global optimization"],"prefix":"10.1007","volume":"8","author":[{"given":"Hong S.","family":"Ryoo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nikolaos V.","family":"Sahinidis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/0377-2217(77)90092-3","volume":"1","author":"S. Albers","year":"1977","unstructured":"Albers, S. and K. Brockhoff (1977), ?A Procedure for New Product Positioning in an Attribute Space,? European Journal of Operational Research, 1, 230?238.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"CR2","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1287\/moor.8.2.273","volume":"8","author":"F. Al-Khayyal","year":"1983","unstructured":"Al-Khayyal, F. and J. E. Falk (1983) ?Jointly Constrained Biconvex Programming,? Mathematics of Operations Research, 8(2), 273?286.","journal-title":"Mathematics of Operations Research"},{"key":"CR3","volume-title":"Very Large Scale Computation in the 21 st Century","author":"G. Anagnostou","year":"1991","unstructured":"Anagnostou, G., E. M. Ronquist, and A. T. Patera (1991), ?A Computational Procedure for Part Design,? in J. P. Mesirov (ed.), Very Large Scale Computation in the 21 st Century, SIAM, Philadelphia."},{"key":"CR4","volume-title":"Control and Dynamic Systems: Advances in Theory and Applications","author":"V. Balakrishnan","year":"1992","unstructured":"Balakrishnan, V. and S. Boyd (1992), Global Optimization in Control System Analysis and Design, in Leondes, C. T. (ed.), Control and Dynamic Systems: Advances in Theory and Applications, vol. 53, Academic Press, New York."},{"key":"CR5","volume-title":"Selected Applications of Nonlinear Programming","author":"J. Bracken","year":"1968","unstructured":"Bracken, J. and G. P. McCormick (1968), Selected Applications of Nonlinear Programming, Wiley, New York."},{"key":"CR6","doi-asserted-by":"crossref","first-page":"1334","DOI":"10.1109\/PROC.1981.12170","volume":"69","author":"R. K. Brayton","year":"1981","unstructured":"Brayton, R. K., G. D. Hachtel, and A. L. Sangiovanni-Vincentelli (1981), ?A Survey of Optimization Techniques for Integrated-Circuit Design,? Proceedings of the IEEE, 69, 1334?1362.","journal-title":"Proceedings of the IEEE"},{"key":"CR7","volume-title":"GAMS-A User's Guide","author":"A. Brooke","year":"1988","unstructured":"Brooke, A., D. Kendrick, and A. Meeraus (1988), GAMS-A User's Guide, The Scientific Press, Redwood City."},{"key":"CR8","unstructured":"Colville, A. R. (1968), ?A Comparative Study of Nonlinear Programming Codes?, IBM Scientific Report 320-2940, New York."},{"issue":"3","key":"CR9","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1007\/BF00940491","volume":"75","author":"G. Danniger","year":"1992","unstructured":"Danniger, G. (1992), ?Role of Copositivity in Optimality Criteria for Nonconvex Optimization Problems,? Journal of Optimization Theory and Applications, 75(3), 535?538.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"CR10","unstructured":"Dixon, L. C. W. (1990), ?On Finding the Global Minimum of a Function of One Variable?, SIAM National Meeting, Chicago, IL."},{"key":"CR11","volume-title":"Towards Global Optimization","author":"L. C. W. Dixon","year":"1975","unstructured":"Dixon, L. C. W. and G. P. Szeg\u00f8 (1975), Towards Global Optimization, North Holland, Amsterdam."},{"key":"CR12","unstructured":"Dur\u00e1n, M. A. (1984), ?A Mixed-integer Nonlinear Programming Approach for the Systematic Synthesis of Engineering Systems?, Ph.D. Thesis, Department of Chemical Engineering, Carnegie Mellon University."},{"key":"CR13","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1002\/aic.690320408","volume":"32","author":"M. A. Dur\u00e1n","year":"1986","unstructured":"Dur\u00e1n, M. A. and I. E. Grossmann (1986), ?A Mixed-integer Nonlinear Programming Algorithm for Process Systems Synthesis,? American Institute of Chemical Engineers Journal, 32, 592?606.","journal-title":"American Institute of Chemical Engineers Journal"},{"key":"CR14","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/BF02592064","volume":"36","author":"M. A. Dur\u00e1n","year":"1986","unstructured":"Dur\u00e1n, M. A. and I. E. Grossmann (1986), ?An Outer-Approximation Algorithm for a Class of Mixed-Integer Nonlinear Programs,? Mathematical Programming, 36, 307?339.","journal-title":"Mathematical Programming"},{"key":"CR15","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1287\/opre.21.1.337","volume":"21","author":"J. E. Falk","year":"1973","unstructured":"Falk, J. E. (1973), ?Conditions for Global Optimality in Nonlinear Programming,? Operations Research, 21, 337?340.","journal-title":"Operations Research"},{"key":"CR16","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1287\/mnsc.15.9.550","volume":"15","author":"J. E. Falk","year":"1969","unstructured":"Falk, J. E. and R. M. Soland (1969), ?An Algorithm for Separable Nonconvex Programming Problems,? Management Science, 15, 550?569.","journal-title":"Management Science"},{"key":"CR17","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1016\/0098-1354(89)87017-6","volume":"13","author":"C. A. Floudas","year":"1989","unstructured":"Floudas, C. A. and A. R. Ciric (1989), ?Strategies for Overcoming Uncertainties in Heat Exchanger Network Synthesis,? Computers & Chemical Engineering, 13, 1133?1152.","journal-title":"Computers & Chemical Engineering"},{"key":"CR18","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-53032-0","volume-title":"A Collection of Test Problems for Constrained Global Optimization Algorithms","author":"C. A. Floudas","year":"1990","unstructured":"Floudas, C. A. and P. M. Pardalos (1990), A Collection of Test Problems for Constrained Global Optimization Algorithms, Springer-Verlag, Berlin."},{"key":"CR19","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1090\/S0025-5718-1971-0312365-X","volume":"25","author":"A. A. Goldstein","year":"1971","unstructured":"Goldstein, A. A. and J. F. Price (1971), ?On Descent from Local Minima,? Mathematics of Computation, 25, 569?574.","journal-title":"Mathematics of Computation"},{"key":"CR20","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/0098-1354(85)80023-5","volume":"9","author":"I. E. Grossmann","year":"1985","unstructured":"Grossmann, I. E. (1985), ?Mixed-integer Programming Approach for the Synthesis of Integrated Process Flow-sheets,? Computers & Chemical Engineering, 9, 463?482.","journal-title":"Computers & Chemical Engineering"},{"key":"CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-2550-5","volume-title":"Elements of Structural Optimization","author":"R. T. Haftka","year":"1992","unstructured":"Haftka, R. T. and Gurdal, Z. (1992), Elements of Structural Optimization, Kluwer Academic Publishers, Dordrecht."},{"issue":"1","key":"CR22","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/BF01100238","volume":"3","author":"A. S. E. Hamed","year":"1993","unstructured":"Hamed, A. S. E. and G. P. McCormick (1993), ?Calculation of Bounds on Variables Satisfying Nonlinear Inequality Constraints,? Journal of Global Optimization, 3(1), 25?47.","journal-title":"Journal of Global Optimization"},{"issue":"2","key":"CR23","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF01582889","volume":"52","author":"P. Hansen","year":"1991","unstructured":"Hansen, P., B. Jaumard, and S.-H. Lu (1991), ?An Analytical Approach to Global Optimization,? Mathematical Programming, 52(2), 227?254.","journal-title":"Mathematical Programming"},{"issue":"4","key":"CR24","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1007\/BF01096413","volume":"3","author":"P. Hansen","year":"1993","unstructured":"Hansen, P., B. Jaumard, and J. Xiong (1993), ?Decomposition and Interval Arithmetic Applied to Global Minimization of Polynomial and Rational Functions,? Journal of Global Optimization, 3(4), 421?437.","journal-title":"Journal of Global Optimization"},{"key":"CR25","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1145\/1111237.1111238","volume":"25","author":"C. A. Haverly","year":"1978","unstructured":"Haverly, C. A. (1978), ?Studies of the Behaviour of Recursion for the Pooling Problem,? SIGMAP Bull., 25, 19.","journal-title":"SIGMAP Bull."},{"key":"CR26","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/BF01442883","volume":"6","author":"R. J. Hillestad","year":"1980","unstructured":"Hillestad, R. J. and S. E. Jacobsen (1980), ?Reverse Convex Programming,? Applied Mathematics and Optimization, 6, 63?78.","journal-title":"Applied Mathematics and Optimization"},{"key":"CR27","first-page":"556","volume":"93","author":"J.-B. Hiriart-Urruty","year":"1986","unstructured":"Hiriart-Urruty, J.-B. (1986), ?When Is a Point x satisfying ?f(x)=0 a global optimum of f?,? American Mathematics Monthly, 93, 556?558.","journal-title":"American Mathematics Monthly"},{"key":"CR28","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02947-3","volume-title":"Global Optimization: Deterministic Approaches","author":"R. Horst","year":"1993","unstructured":"Horst, R. and H. Tuy (1993), Global Optimization: Deterministic Approaches, Springer-Verlag, 2nd ed., Berlin.","edition":"2nd ed."},{"issue":"3","key":"CR29","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1287\/moor.12.3.544","volume":"12","author":"B. Kalantari","year":"1987","unstructured":"Kalantari, B. and J. B. Rosen (1987), ?An Algorithm for Global Minimization of Linearly Constrained Convex Quadratic Functions,? Mathematics of Operations Research, 12(3), 544?561.","journal-title":"Mathematics of Operations Research"},{"issue":"8","key":"CR30","doi-asserted-by":"crossref","first-page":"1407","DOI":"10.1021\/ie00080a013","volume":"27","author":"G. R. Kocis","year":"1988","unstructured":"Kocis, G. R. and I. E. Grossmann (1988), ?Global Optimization of Nonconvex MINLP Problems in Process Synthesis,? Industrial and Engineering Chemistry Research, 27(8), 1407?1421.","journal-title":"Industrial and Engineering Chemistry Research"},{"key":"CR31","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF02283691","volume":"25","author":"H. Konno","year":"1990","unstructured":"Konno, H. and T. Kuno (1990), ?Generalized Linear Multiplicative and Fractional Programming,? Annals of Operations Research, 25, 147?162.","journal-title":"Annals of Operations Research"},{"key":"CR32","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF00253808","volume":"1","author":"H. Konno","year":"1992","unstructured":"Konno, H., T. Kuno, and Y. Yajima (1992), ?Parametric Simplex Algorithms for a Class of NP-Complete Problems Whose Average Number of Steps is Polynomial,? Computational Optimization and Applications, 1, 227?239.","journal-title":"Computational Optimization and Applications"},{"issue":"3","key":"CR33","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1007\/BF00119935","volume":"1","author":"T. Kuno","year":"1991","unstructured":"Kuno, T. and H. Konno (1991), ?A Parametric Successive Underestimation Method for Convex Multiplicative Programming Problems,? Journal of Global Optimization, 1(3), 267?285.","journal-title":"Journal of Global Optimization"},{"issue":"3","key":"CR34","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/BF01096771","volume":"3","author":"B. W. Lamar","year":"1993","unstructured":"Lamar, B. W. (1993), ?An Improved Branch and Bound Algorithm for Minimum Concave Cost Network Flow Problems,? Journal of Global Optimization, 3(3), 261?287.","journal-title":"Journal of Global Optimization"},{"issue":"no. ST11","key":"CR35","doi-asserted-by":"crossref","first-page":"2177","DOI":"10.1061\/JSDEAG.0005816","volume":"107","author":"J. Liebman","year":"1981","unstructured":"Liebman, J., N. Khachaturian, and V. Chanaratna (1981), ?Discrete Structural Optimization,? Journal of Structural Division, ASCE, 107, no. ST11, Proceedings paper 16643 (Nov.), 2177?2197.","journal-title":"Journal of Structural Division, ASCE"},{"key":"CR36","volume-title":"Modeling and Optimization with GINO","author":"J. Liebman","year":"1986","unstructured":"Liebman, J., L. Lasdon, L. Schrage, and A. Waren (1986), Modeling and Optimization with GINO, The Scientific Press, Palo Alto, CA."},{"key":"CR37","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1080\/00986449208936033","volume":"115","author":"M. Manousiouthakis","year":"1992","unstructured":"Manousiouthakis, M. and D. Sourlas (1992), ?A Global Optimization Approach to Rationally Constrained Rational Programming,? Chemical Engineering Communications, 115, 127?147.","journal-title":"Chemical Engineering Communications"},{"key":"CR38","series-title":"Technical Report Serial T-267","volume-title":"Converting General Nonlinear Programming Problems to Separable Nonlinear Programming Problems","author":"G. P. McCormick","year":"1972","unstructured":"McCormick, G. P. (1972), ?Converting General Nonlinear Programming Problems to Separable Nonlinear Programming Problems,? Technical Report Serial T-267, The George Washington University, Washington, D.C."},{"key":"CR39","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF01580665","volume":"10","author":"G. P. McCormick","year":"1976","unstructured":"McCormick, G. P. (1976), ?Computability of Global Solutions to Factorable Nonconvex Programs: Part I-Convex Underestimating Problsms,? Mathematical Programming, 10, 147?175.","journal-title":"Mathematical Programming"},{"key":"CR40","volume-title":"Nonlinear Programming. Theory, Algorithms, and Applications","author":"G. P. McCormick","year":"1983","unstructured":"McCormick, G. P. (1983), Nonlinear Programming. Theory, Algorithms, and Applications, Wiley Interscience, New York."},{"key":"CR41","volume-title":"Mathematical Programming. Theory and Algorithms","author":"M. Minoux","year":"1986","unstructured":"Minoux, M. (1986), Mathematical Programming. Theory and Algorithms, Wiley, New York."},{"key":"CR42","volume-title":"Interval Analysis","author":"R. Moore","year":"1966","unstructured":"Moore, R. (1966), Interval Analysis, Prentice Hall, Englewood Cliffs, New Jersey."},{"key":"CR43","series-title":"Technical Report SOL 83-20","volume-title":"MINOS 5.0 User's Guide","author":"B. A. Murtagh","year":"1986","unstructured":"Murtagh, B. A. and M. A. Saunders (1986), MINOS 5.0 User's Guide, Technical Report SOL 83?20, Systems Optimization Laboratory, Department of Operations Research, Stanford University, CA."},{"key":"CR44","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/BF02592948","volume":"39","author":"K. G. Murty","year":"1987","unstructured":"Murty, K. G. and S. N. Kabadi (1987), ?Some NP-Complete Problems in Quadratic and Nonlinear Programming,? Mathematical Programming, 39, 117?129.","journal-title":"Mathematical Programming"},{"issue":"2","key":"CR45","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/BF00122055","volume":"2","author":"A. Neumaier","year":"1992","unstructured":"Neumaier, A. (1992), ?An Optimal Criterion for Global Quadratic Optimization,? Journal of Global Optimization, 2(2), 201?208.","journal-title":"Journal of Global Optimization"},{"key":"CR46","unstructured":"Papalambros, P. Y. and D. J. Wilde (1988), Principles of Optimal Design, Cambridge University Press."},{"issue":"6","key":"CR47","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1080\/02331939008843615","volume":"21","author":"P. M. Pardalos","year":"1990","unstructured":"Pardalos, P. M. (1990), ?Polynomial Time Algorithms for Some Classes of Constrained Quadratic Problems,? Optimization, 21(6), 843?853.","journal-title":"Optimization"},{"key":"CR48","volume-title":"Handbook of Global Optimization","author":"P. M. Pardalos","year":"1994","unstructured":"Pardalos, P. M. and R. Horst (1994), Handbook of Global Optimization, Kluwer Academic Publishers, Norwell (Massachusetts)."},{"key":"CR49","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/0167-6377(88)90049-1","volume":"7","author":"P. M. Pardalos","year":"1988","unstructured":"Pardalos, P. M. and G. Schnitger (1988), ?Checking local optimality in constrained quadratic programming is NP-hard,? Operations Research Letters, 7, 33?35.","journal-title":"Operations Research Letters"},{"issue":"2","key":"CR50","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/BF01096719","volume":"4","author":"P. M. Pardalos","year":"1994","unstructured":"Pardalos, P. M., D. Shalloway, and G. Xue (1994), ?Optimization Methods for Computing Global Minima of Nonconvex Potential Energy Functions,? Journal of Global Optimization, 4(2), 117?133.","journal-title":"Journal of Global Optimization"},{"key":"CR51","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1002\/1520-6750(199008)37:4<499::AID-NAV3220370405>3.0.CO;2-9","volume":"37","author":"A. T. Phillips","year":"1990","unstructured":"Phillips, A. T. and J. B. Rosen (1990), ?Guaranteed ?-Approximate Solution for Indefinite Quadratic Global Minimization,? Naval Research Logistics, 37, 499?514.","journal-title":"Naval Research Logistics"},{"key":"CR52","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-1161-1","volume-title":"Structural Design via Optimality Criteria","author":"G. I. N. Rozvany","year":"1989","unstructured":"Rozvany, G. I. N. (1989), Structural Design via Optimality Criteria, Kluwer Academic Publishers, Dordrecht."},{"key":"CR53","unstructured":"Ryoo, H. S. (1994), ?Range Reduction as a Means of Performance Improvement in Global Optimization: A Branch-and-Reduce Global Optimization Algorithm?, Master's Thesis, University of Illinois at Urbana-Champaign, IL."},{"issue":"5","key":"CR54","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/0098-1354(94)00097-2","volume":"19","author":"H. S. Ryoo","year":"1995","unstructured":"Ryoo, H. S. and N. V. Sahinidis (1995), ?Global Optimization of Nonconvex NLPs and MINLPs with Applications in Process Design,? Computer & Chemical Engineering, 19(5), 551?566.","journal-title":"Computer & Chemical Engineering"},{"issue":"7","key":"CR55","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/0098-1354(91)85027-R","volume":"15","author":"N. V. Sahinidis","year":"1991","unstructured":"Sahinidis, N. V. and I. E. Grossmann (1991), ?Convergence Properties of Generalized Benders Decomposition,? Computers & Chemical Engineering, 15(7), 481?491.","journal-title":"Computers & Chemical Engineering"},{"issue":"3","key":"CR56","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF00119932","volume":"1","author":"F. Schoen","year":"1991","unstructured":"Schoen, F. (1991), ?Stochastic Techniques for Global Optimization: A Survey of Recent Advances,? Journal of Global Optimization, 1(3), 207?228.","journal-title":"Journal of Global Optimization"},{"issue":"4","key":"CR57","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/BF00122429","volume":"2","author":"H. D. Sherali","year":"1992","unstructured":"Sherali, H. D. and A. Alameddine (1992), ?A new Reformulation-Linearization Technique for Bilinear Programming Problems,? Journal of Global Optimization, 2(4), 379?410.","journal-title":"Journal of Global Optimization"},{"key":"CR58","series-title":"Technical Report","volume-title":"Tight Reformulation-Linearization Technique Representations for Solving Nonconvex Quadratic Programming Problems","author":"H. D. Sherali","year":"1994","unstructured":"Sherali, H. D. and C. H. Tuncbilek (1994), ?Tight Reformulation-Linearization Technique Representations for Solving Nonconvex Quadratic Programming Problems,? Technical Report, Virginia Polytechnic Institute and State University, Blacksburg, Virginia."},{"issue":"11","key":"CR59","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1287\/mnsc.17.11.759","volume":"17","author":"R. M. Soland","year":"1971","unstructured":"Soland, R. M. (1971), ?An Algorithm for Separable Nonconvex Programming Problems II: Nonconvex Constraints,? Management Science, 17(11), 759?773.","journal-title":"Management Science"},{"issue":"3","key":"CR60","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/BF00933339","volume":"15","author":"G. Stephanopoulos","year":"1975","unstructured":"Stephanopoulos, G. and A. W. Westerberg (1975), ?The Use of Hestenes' Method of Multipliers to Resolve Dual Gaps in Engineering System Optimization,? Journal of Optimization Theory and Applications, 15(3), 285?309.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"CR61","volume-title":"Design of Thermal Systems","author":"W.F. Stoecker","year":"1971","unstructured":"Stoecker, W.F. (1971), Design of Thermal Systems, McGraw-Hill Book Co., New York."},{"key":"CR62","unstructured":"Swaney, R. E. (1990), ?Global Solution of Algebraic Nonlinear Programs?, AIChE Annual Meeting, Chicago, IL."},{"issue":"2","key":"CR63","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1287\/moor.16.2.390","volume":"16","author":"L. S. Thakur","year":"1990","unstructured":"Thakur, L. S. (1990), ?Domain Contraction in Nonlinear Programming: Minimizing a Quadratic Concave Function Over a Polyhedron,? Mathematics of Operations Research, 16(2), 390?407.","journal-title":"Mathematics of Operations Research"},{"issue":"4","key":"CR64","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF00130830","volume":"1","author":"N. V. Thoai","year":"1991","unstructured":"Thoai, N. V. (1991), ?A Global Optimization Approach for Solving the Convex Multiplicative Programming Problem,? Journal of Global Optimization, 1(4), 341?357.","journal-title":"Journal of Global Optimization"},{"key":"CR65","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-50871-6","volume-title":"Global Optimization","author":"A. T\u00f6rn","year":"1989","unstructured":"T\u00f6rn, A. and A. Zilinskas (1989), Global Optimization, Lecture Notes in Computer Science, 350, Springer-Verlag, Berlin."},{"key":"CR66","first-page":"32","volume":"159","author":"H. Tuy","year":"1964","unstructured":"Tuy, H. (1964), ?Concave Programming Under Linear Constraints,? Doklady Akademic Nauk, 159, 32?35. Translated Soviet Mathematics, 5, 1437?1440.","journal-title":"Doklady Akademic Nauk"},{"key":"CR67","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1007\/BF00938217","volume":"52","author":"H. Tuy","year":"1987","unstructured":"Tuy, H. (1987), ?Convex Programs with an additional reverse convex constraint,? Journal of Optimization Theory and Applications, 52, 463?486.","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"1","key":"CR68","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/BF00120663","volume":"1","author":"H. Tuy","year":"1991","unstructured":"Tuy, H. (1991), ?Effect of the Subdivision Strategy on Convergence and Efficiency of Some Global Optimization Algorithms,? Journal of Global Optimization, 1(1), 23?36.","journal-title":"Journal of Global Optimization"},{"issue":"2","key":"CR69","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01580762","volume":"41","author":"H. Tuy","year":"1988","unstructured":"Tuy, H. and R. Horst (1988), ?Convergence and Restart in Branch-and-Bound Algorithms for Global Optimization. Application to Concave Minimization and D.C. Optimization Problems,? Mathematical Programming, 41(2), 161?183.","journal-title":"Mathematical Programming"},{"issue":"6","key":"CR70","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1080\/02331938708843294","volume":"18","author":"H. Tuy","year":"1987","unstructured":"Tuy, H., V. Khatchaturov, and S. Utkin (1987), ?A Class of Exhaustive Cone Splitting Procedures in Conical Algorithms for Concave Minimization,? Optimization, 18(6), 791?807.","journal-title":"Optimization"},{"issue":"2","key":"CR71","doi-asserted-by":"crossref","first-page":"1419","DOI":"10.1016\/0098-1354(90)80021-3","volume":"14","author":"V. Visweswaran","year":"1990","unstructured":"Visweswaran, V. and C. A. Floudas (1990), ?A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs-II. Application of Theory and Test Problems,? Computers & Chemical Engineering, 14(2), 1419?1434.","journal-title":"Computers & Chemical Engineering"},{"key":"CR72","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0098-1354(78)80012-X","volume":"2","author":"A. W. Westerberg","year":"1978","unstructured":"Westerberg, A. W. and J. V. Shah (1978), ?Assuring a Global Optimum by the Use of an Upper Bound on the Lower (Dual) Bound,? Computers & Chemical Engineering, 2, 83?92.","journal-title":"Computers & Chemical Engineering"},{"key":"CR73","volume-title":"Globally Optimal Design","author":"D. J. Wilde","year":"1978","unstructured":"Wilde, D. J. (1978), Globally Optimal Design, J. Wiley & Sons, New York."},{"key":"CR74","volume-title":"Rounding Errors in Algebraic Processes","author":"J. H. Wilkinson","year":"1963","unstructured":"Wilkinson, J. H. (1963), Rounding Errors in Algebraic Processes, Prentice Hall, Englewood Cliffs, New Jersey."},{"key":"CR75","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1080\/00207168508803469","volume":"17","author":"D. R. Wingo","year":"1985","unstructured":"Wingo, D. R. (1985), ?Globally Minimizing Polynomials without Evaluating Derivatives,? International Journal of Computer Mathematics, 17, 287?294.","journal-title":"International Journal of Computer Mathematics"},{"issue":"4","key":"CR76","first-page":"331","volume":"22","author":"X. Yuan","year":"1988","unstructured":"Yuan, X., S. Zhang, L. Pibouleau and S. Domenech (1988), ?Une m\u00e9thode d'optimisation non lin\u00e9aire en variables mixtes pour la conception de proc\u00e9d\u00e9s,? Recherche Op\u00e9rataionnelle\/Operations Research, 22(4), 331?346.","journal-title":"Recherche Op\u00e9rataionnelle\/Operations Research"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF00138689.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF00138689\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF00138689","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,27]],"date-time":"2021-06-27T14:18:27Z","timestamp":1624803507000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF00138689"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3]]},"references-count":76,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1996,3]]}},"alternative-id":["BF00138689"],"URL":"https:\/\/doi.org\/10.1007\/bf00138689","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,3]]}}}