{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T06:49:32Z","timestamp":1764053372188},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,9,23]],"date-time":"2014-09-23T00:00:00Z","timestamp":1411430400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2016,2]]},"DOI":"10.1007\/s11590-014-0799-6","type":"journal-article","created":{"date-parts":[[2014,9,23]],"date-time":"2014-09-23T23:53:58Z","timestamp":1411516438000},"page":"283-308","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Performance of convex underestimators in a branch-and-bound framework"],"prefix":"10.1007","volume":"10","author":[{"given":"Yannis A.","family":"Guzman","sequence":"first","affiliation":[]},{"given":"M. M. Faruque","family":"Hasan","sequence":"additional","affiliation":[]},{"given":"Christodoulos A.","family":"Floudas","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,9,23]]},"reference":[{"key":"799_CR1","unstructured":"IBM: IBM ILOG CPLEX Optimization Studio (2013). http:\/\/www.cplex.com"},{"key":"799_CR2","doi-asserted-by":"crossref","unstructured":"Adjiman, C.S., Androulakis, I.P., Floudas, C.A.: A global optimization method, $$\\alpha $$ \u03b1 BB, for general twice-differentiable constrained NLPs-II. Implementation and computational results. Comput. Chem. Eng. 22(9), 1159\u20131179 (1998b)","DOI":"10.1016\/S0098-1354(98)00218-X"},{"key":"799_CR3","doi-asserted-by":"crossref","unstructured":"Adjiman, C.S., Dallwig, S., Floudas, C.A., Neumaier, A.: A global optimization method, $$\\alpha $$ \u03b1 BB, for general twice-differentiable constrained NLPs-I. Theoretical advances. Comput. Chem. Eng. 22(9), 1137\u20131158 (1998a)","DOI":"10.1016\/S0098-1354(98)00027-1"},{"issue":"1","key":"799_CR4","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/BF00121749","volume":"9","author":"CS Adjiman","year":"1996","unstructured":"Adjiman, C.S., Floudas, C.A.: Rigorous convex underestimators for general twice-differentiable problems. J. Global Optim. 9(1), 23\u201340 (1996)","journal-title":"J. Global Optim."},{"key":"799_CR5","doi-asserted-by":"crossref","unstructured":"Akrotirianakis, I.G., Floudas, C.A.: A new class of improved convex underestimators for twice continuously differentiable constrained NLPs. J. Global Optim. 30(4), 367\u2013390 (2004a)","DOI":"10.1007\/s10898-004-6455-4"},{"key":"799_CR6","doi-asserted-by":"crossref","unstructured":"Akrotirianakis, I.G., Floudas, C.A.: Computational experience with a new class of convex underestimators: Box-constrained NLP problems. J. Global Optim. 29(3), 249\u2013264 (2004b)","DOI":"10.1023\/B:JOGO.0000044768.75992.10"},{"issue":"2","key":"799_CR7","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1287\/moor.8.2.273","volume":"8","author":"FA Al-Khayyal","year":"1983","unstructured":"Al-Khayyal, F.A., Falk, J.E.: Jointly constrained biconvex programming. Math. Oper. Res. 8(2), 273\u2013286 (1983)","journal-title":"Math. Oper. Res."},{"issue":"4","key":"799_CR8","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.: $$\\alpha $$ \u03b1 BB: a global optimization method for general constrained nonconvex problems. J. Global Optim. 7(4), 337\u2013363 (1995)","journal-title":"J. Global Optim."},{"key":"799_CR9","unstructured":"Bendtsen, C., Stauning, O.: Fadbad, a flexible C++ package for automatic differentiation. Department of Mathematical Modelling, Technical University of Denmark (1996)"},{"issue":"1","key":"799_CR10","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1215\/S0012-7094-47-01403-8","volume":"14","author":"A Brauer","year":"1947","unstructured":"Brauer, A.: Limits for the characteristic roots of a matrix. II. Duke Math. J. 14(1), 21\u201326 (1947)","journal-title":"Duke Math. J."},{"key":"799_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4949-6","volume-title":"Deterministic Global Optimization: Theory, Methods and Applications","author":"CA Floudas","year":"2000","unstructured":"Floudas, C.A.: Deterministic Global Optimization: Theory, Methods and Applications, vol. 37. Springer, Berlin (2000)"},{"key":"799_CR12","doi-asserted-by":"crossref","unstructured":"Floudas, C.A., Pardalos, P.M., Adjiman, C.S., Esposito, W.R., Gumus, Z.H., Harding, S.T., Klepeis, J.L., Meyer, C.A., Schweiger, C.A.: Handbook of Test Problems in Local and Global Optimization, vol. 33. Kluwer Academic Publishers, Dordrecht (1999)","DOI":"10.1007\/978-1-4757-3040-1"},{"key":"799_CR13","first-page":"749","volume":"6","author":"SA Gershgorin","year":"1931","unstructured":"Gershgorin, S.A.: \u00dcber die abgrenzung der eigenwerte einer matrix. Izv. Akad. Nauk SSSR, Ser. Fiz.-Mat. 6, 749\u2013754 (1931)","journal-title":"Izv. Akad. Nauk SSSR, Ser. Fiz.-Mat."},{"key":"799_CR14","unstructured":"Gill, P.E., Murray, W., Saunders, M.A.: User\u2019s guide for SNOPT 5.3: a Fortran package for large-scale nonlinear programming. Technical Report (1999)"},{"key":"799_CR15","doi-asserted-by":"crossref","unstructured":"Gill, P.E., Murray, W., Saunders, M.A., Wright, M.H.: User\u2019s guide for NPSOL (Version 4.0): a Fortran package for nonlinear programming. Technical Report, DTIC Document (1986)","DOI":"10.21236\/ADA169115"},{"issue":"1","key":"799_CR16","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s10898-008-9288-8","volume":"42","author":"CE Gounaris","year":"2008","unstructured":"Gounaris, C.E., Floudas, C.A.: Tight convex underestimators for $${\\cal {C}}^2$$ C 2 -continuous problems: II. Multivariate functions. J. Global Optim. 42(1), 69\u201389 (2008)","journal-title":"J. Global Optim."},{"issue":"1","key":"799_CR17","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1023\/A:1009917818868","volume":"3","author":"ER Hansen","year":"1997","unstructured":"Hansen, E.R.: Sharpness in interval computations. Reliab. Comput. 3(1), 17\u201329 (1997)","journal-title":"Reliab. Comput."},{"key":"799_CR18","unstructured":"Hlad\u00edk, M.: The effect of hessian evaluations in the global optimization $$\\alpha $$ \u03b1 BB method, Preprint (2013). http:\/\/arxiv.org\/abs\/1307.2791"},{"issue":"16","key":"799_CR19","doi-asserted-by":"crossref","first-page":"4042","DOI":"10.1016\/j.cam.2012.02.020","volume":"236","author":"DE Kvasov","year":"2012","unstructured":"Kvasov, D.E., Sergeyev, Y.D.: Lipschitz gradients for global optimization in a one-point-based partitioning scheme. J. Comput. Appl. Math. 236(16), 4042\u20134054 (2012)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"799_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10898-012-9974-4","volume":"56","author":"J Lasserre","year":"2013","unstructured":"Lasserre, J., Thanh, T.: Convex underestimators of polynomials. J. Global Optim. 56(1), 1\u201325 (2013)","journal-title":"J. Global Optim."},{"issue":"1","key":"799_CR21","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1137\/110859129","volume":"23","author":"D Lera","year":"2013","unstructured":"Lera, D., Sergeyev, Y.D.: Acceleration of univariate global optimization algorithms working with lipschitz functions and lipschitz first derivatives. SIAM J. Optim. 23(1), 508\u2013529 (2013)","journal-title":"SIAM J. Optim."},{"issue":"10","key":"799_CR22","doi-asserted-by":"crossref","first-page":"7667","DOI":"10.1063\/1.463486","volume":"97","author":"CD Maranas","year":"1992","unstructured":"Maranas, C.D., Floudas, C.A.: A global optimization approach for Lennard\u2013Jones microclusters. J. Chem. Phys. 97(10), 7667\u20137678 (1992)","journal-title":"J. Chem. Phys."},{"issue":"2","key":"799_CR23","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1063\/1.467236","volume":"100","author":"CD Maranas","year":"1994","unstructured":"Maranas, C.D., Floudas, C.A.: A deterministic global optimization approach for molecular structure determination. J. Chem. Phys. 100(2), 1247\u20131261 (1994a)","journal-title":"J. Chem. Phys."},{"issue":"2","key":"799_CR24","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/BF01096720","volume":"4","author":"CD Maranas","year":"1994","unstructured":"Maranas, C.D., Floudas, C.A.: Global minimum potential energy conformations of small molecules. J. Global Optim. 4(2), 135\u2013170 (1994)","journal-title":"J. Global Optim."},{"issue":"2","key":"799_CR25","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/BF01097059","volume":"7","author":"CD Maranas","year":"1995","unstructured":"Maranas, C.D., Floudas, C.A.: Finding all solutions of nonlinearly constrained systems of equations. J. Global Optim. 7(2), 143\u2013182 (1995)","journal-title":"J. Global Optim."},{"issue":"1","key":"799_CR26","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF01580665","volume":"10","author":"GP McCormick","year":"1976","unstructured":"McCormick, G.P.: Computability of global solutions to factorable nonconvex programs: Part I\u2014convex underestimating problems. Math. Program. 10(1), 147\u2013175 (1976)","journal-title":"Math. Program."},{"key":"799_CR27","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/978-1-4613-0251-3_18","volume":"74","author":"CA Meyer","year":"2003","unstructured":"Meyer, C.A., Floudas, C.A.: Trilinear monomials with positive or negative domains: facets of the convex and concave envelopes. Nonconvex Optim. Appl. 74, 327\u2013352 (2003)","journal-title":"Nonconvex Optim. Appl."},{"issue":"2","key":"799_CR28","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1023\/B:JOGO.0000042112.72379.e6","volume":"29","author":"CA Meyer","year":"2004","unstructured":"Meyer, C.A., Floudas, C.A.: Trilinear monomials with mixed sign domains: facets of the convex and concave envelopes. J. Global Optim. 29(2), 125\u2013155 (2004)","journal-title":"J. Global Optim."},{"issue":"2","key":"799_CR29","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s10898-004-2704-9","volume":"32","author":"CA Meyer","year":"2005","unstructured":"Meyer, C.A., Floudas, C.A.: Convex underestimation of twice continuously differentiable functions by piecewise quadratic perturbation: spline $$\\alpha $$ \u03b1 BB underestimators. J. Global Optim. 32(2), 221\u2013258 (2005)","journal-title":"J. Global Optim."},{"issue":"3","key":"799_CR30","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1512\/iumj.1993.42.42045","volume":"42","author":"M Putinar","year":"1993","unstructured":"Putinar, M.: Positive polynomials on compact semi-algebraic sets. Indiana Univ. Math. J. 42(3), 969\u2013984 (1993)","journal-title":"Indiana Univ. Math. J."},{"issue":"S3","key":"799_CR31","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1002\/zamm.19980781593","volume":"78","author":"J Rohn","year":"1998","unstructured":"Rohn, J.: Bounds on eigenvalues of interval matrices. Zeitschrift fr Angewandte Mathematik und Mechanik 78(S3), 1049\u20131050 (1998)","journal-title":"Zeitschrift fr Angewandte Mathematik und Mechanik"},{"key":"799_CR32","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-8042-6","volume-title":"Introduction to Global Optimization Exploiting Space-Filling Curves","author":"YD Sergeyev","year":"2013","unstructured":"Sergeyev, Y.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer, Berlin (2013)"},{"issue":"3","key":"799_CR33","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/s10898-013-0057-y","volume":"58","author":"A Skj\u00e4l","year":"2014","unstructured":"Skj\u00e4l, A., Westerlund, T.: New methods for calculating $$\\alpha $$ \u03b1 BB-type underestimators. J. Global Optim. 58(3), 411\u2013427 (2014)","journal-title":"J. Global Optim."},{"issue":"2","key":"799_CR34","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1007\/s10957-012-0033-6","volume":"154","author":"A Skj\u00e4l","year":"2012","unstructured":"Skj\u00e4l, A., Westerlund, T., Misener, R., Floudas, C.: A generalization of the classical $$\\alpha $$ \u03b1 BB convex underestimation via diagonal and nondiagonal quadratic terms. J. Optim. Theory Appl. 154(2), 462\u2013490 (2012)","journal-title":"J. Optim. Theory Appl."},{"key":"799_CR35","unstructured":"Surjanovic, S., Bingham, D.: Virtual library of simulation experiments: test functions and datasets (2013). http:\/\/www.sfu.ca\/~ssurjano\/optimization.html"},{"issue":"2","key":"799_CR36","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1023\/A:1011233805045","volume":"20","author":"M Tawarmalani","year":"2001","unstructured":"Tawarmalani, M., Sahinidis, N.V.: Semidefinite relaxations of fractional programs via novel convexification techniques. J. Global Optim. 20(2), 133\u2013154 (2001)","journal-title":"J. Global Optim."},{"issue":"2","key":"799_CR37","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s10107-002-0308-z","volume":"93","author":"M Tawarmalani","year":"2002","unstructured":"Tawarmalani, M., Sahinidis, N.V.: Convex extensions and envelopes of lower semi-continuous functions. Math. Program. 93(2), 247\u2013263 (2002)","journal-title":"Math. Program."},{"issue":"2","key":"799_CR38","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1002\/spe.626","volume":"35","author":"RC Whaley","year":"2005","unstructured":"Whaley, R.C., Petitet, A.: Minimizing development and maintenance costs in supporting persistently optimized BLAS. Softw. Pract. Experience 35(2), 101\u2013121 (2005)","journal-title":"Softw. Pract. Experience"},{"key":"799_CR39","unstructured":"Yamashita, M., Fujisawa, K., Nakata, K., Nakata, M., Fukuda, M., Kobayashi, K., Goto, K.: A high-performance software package for semidefinite programs: SDPA 7. Technical Report B-460, Department of Mathematical and Computing Science, Tokyo Institute of Technology, Tokyo, Japan (2010)"}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-014-0799-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-014-0799-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-014-0799-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,15]],"date-time":"2019-08-15T09:22:08Z","timestamp":1565860928000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-014-0799-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,23]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,2]]}},"alternative-id":["799"],"URL":"https:\/\/doi.org\/10.1007\/s11590-014-0799-6","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,23]]}}}