{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:21:09Z","timestamp":1740122469068,"version":"3.37.3"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T00:00:00Z","timestamp":1547164800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/J003840\/1"],"award-info":[{"award-number":["EP\/J003840\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2019,3]]},"DOI":"10.1007\/s10898-018-0718-y","type":"journal-article","created":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T13:41:55Z","timestamp":1547214115000},"page":"467-483","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Tighter $$\\alpha $$ \u03b1 BB relaxations through a refinement scheme for the scaled Gerschgorin theorem"],"prefix":"10.1007","volume":"73","author":[{"given":"Dimitrios","family":"Nerantzis","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4573-7722","authenticated-orcid":false,"given":"Claire S.","family":"Adjiman","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,1,11]]},"reference":[{"issue":"9","key":"718_CR1","doi-asserted-by":"publisher","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, $$\\alpha $$ \u03b1 BB, for general twice-differentiable constrained NLPs-II. Implementation and computational results. Comput. Chem. Eng. 22(9), 1159\u20131179 (1998)","journal-title":"Comput. Chem. Eng."},{"key":"718_CR2","doi-asserted-by":"publisher","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, $$\\alpha $$ \u03b1 BB, for general twice-differentiable constrained NLPs I. Theor. Adv. Comput. Chem. Eng. 22, 1137\u20131158 (1998)","journal-title":"Theor. Adv. Comput. Chem. Eng."},{"issue":"3","key":"718_CR3","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1023\/B:JOGO.0000044768.75992.10","volume":"29","author":"IG Akrotirianakis","year":"2004","unstructured":"Akrotirianakis, I.G., Floudas, C.A.: Computational experience with a new class of convex underestimators: box-constrained NLP problems. J. Glob. Optim. 29(3), 249\u2013264 (2004)","journal-title":"J. Glob. Optim."},{"issue":"4","key":"718_CR4","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1007\/s10898-004-6455-4","volume":"30","author":"IG Akrotirianakis","year":"2004","unstructured":"Akrotirianakis, I.G., Floudas, C.A.: A new class of improved convex underestimators for twice continuously differentiable constrained NLPs. J. Glob. Optim. 30(4), 367\u2013390 (2004)","journal-title":"J. Glob. Optim."},{"issue":"4","key":"718_CR5","doi-asserted-by":"publisher","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. Glob. Optim. 7(4), 337\u2013363 (1995)","journal-title":"J. Glob. Optim."},{"key":"718_CR6","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1137\/0126013","volume":"26","author":"D Carlson","year":"1974","unstructured":"Carlson, D., Haynsworth, E., Markham, T.: A generalization of the Schur complement by means of the Moore\u2013Penrose inverse. SIAM J. Appl. Math. 26, 169\u2013175 (1974)","journal-title":"SIAM J. Appl. Math."},{"key":"718_CR7","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/0024-3795(74)90066-4","volume":"8","author":"RW Cottle","year":"1974","unstructured":"Cottle, R.W.: Manifestations of the Schur complement. Linear Algebra Appl. 8, 189\u2013211 (1974)","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"718_CR8","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/BF01096455","volume":"5","author":"K Du","year":"1994","unstructured":"Du, K., Kearfott, R.B.: The cluster problem in multivariate global optimization. J. Glob. Optim. 5(3), 253\u2013265 (1994)","journal-title":"J. Glob. Optim."},{"issue":"2","key":"718_CR9","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/s11590-014-0799-6","volume":"10","author":"YA Guzman","year":"2014","unstructured":"Guzman, Y.A., Hasan, M.F., Floudas, C.A.: Performance of convex underestimators in a branch-and-bound framework. Optim. Lett. 10(2), 283\u2013308 (2014)","journal-title":"Optim. Lett."},{"key":"718_CR10","doi-asserted-by":"crossref","DOI":"10.1201\/9780203026922","volume-title":"Global Optimization Using Interval Analysis. Pure and Applied Mathematics","author":"E Hansen","year":"2003","unstructured":"Hansen, E., Walster, G.: Global Optimization Using Interval Analysis. Pure and Applied Mathematics. M. Dekker, New York (2003)"},{"issue":"1","key":"718_CR11","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/0024-3795(68)90050-5","volume":"1","author":"EV Haynsworth","year":"1968","unstructured":"Haynsworth, E.V.: Determination of the inertia of a partitioned Hermitian matrix. Linear Algebra Appl. 1(1), 73\u201381 (1968)","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"718_CR12","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1109\/9.126593","volume":"37","author":"D Hertz","year":"1992","unstructured":"Hertz, D.: The extreme eigenvalues and stability of real symmetric interval matrices. IEEE Trans. Autom. Control 37(4), 532\u2013535 (1992)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"4","key":"718_CR13","doi-asserted-by":"publisher","first-page":"2116","DOI":"10.1137\/090753991","volume":"31","author":"M Hlad\u00edk","year":"2010","unstructured":"Hlad\u00edk, M., Daney, D., Tsigaridas, E.P.: Bounds on real eigenvalues and singular values of interval matrices. SIAM J. Matrix Anal. Appl. 31(4), 2116\u20132129 (2010)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"1","key":"718_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10898-012-9974-4","volume":"56","author":"JB Lasserre","year":"2013","unstructured":"Lasserre, J.B., Thanh, T.P.: Convex underestimators of polynomials. J. Glob. Optim. 56(1), 1\u201325 (2013)","journal-title":"J. Glob. Optim."},{"issue":"2","key":"718_CR15","doi-asserted-by":"publisher","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 (1994)","journal-title":"J. Chem. Phys."},{"issue":"2","key":"718_CR16","doi-asserted-by":"publisher","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. Glob. Optim. 32(2), 221\u2013258 (2005)","journal-title":"J. Glob. Optim."},{"key":"718_CR17","doi-asserted-by":"publisher","first-page":"1407","DOI":"10.1016\/S0098-1354(98)80031-8","volume":"22","author":"CA Meyer","year":"1998","unstructured":"Meyer, C.A., Swartz, C.L.E.: A regional convexity test for global optimization: application to the phase equilibrium problem. Comput. Chem. Eng. 22, 1407\u20131418 (1998)","journal-title":"Comput. Chem. Eng."},{"key":"718_CR18","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/s10898-016-0430-8","volume":"67","author":"D Nerantzis","year":"2016","unstructured":"Nerantzis, D., Adjiman, C.S.: Enclosure of all index-1 saddle points of general nonlinear functions. J. Glob. Optim. 67, 451\u2013474 (2016). https:\/\/doi.org\/10.1007\/s10898-016-0430-8","journal-title":"J. Glob. Optim."},{"issue":"3","key":"718_CR19","doi-asserted-by":"publisher","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. Glob. Optim. 58(3), 411\u2013427 (2014)","journal-title":"J. Glob. Optim."},{"issue":"2","key":"718_CR20","doi-asserted-by":"publisher","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.: 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."},{"issue":"3","key":"718_CR21","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1007\/s10898-013-0059-9","volume":"58","author":"A Wechsung","year":"2014","unstructured":"Wechsung, A., Schaber, S.D., Barton, P.I.: The cluster problem revisited. J. Glob. Optim. 58(3), 429\u2013438 (2014)","journal-title":"J. Glob. Optim."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-018-0718-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-0718-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-0718-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,10]],"date-time":"2022-09-10T03:31:45Z","timestamp":1662780705000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-018-0718-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,11]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["718"],"URL":"https:\/\/doi.org\/10.1007\/s10898-018-0718-y","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2019,1,11]]},"assertion":[{"value":"3 January 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 October 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 January 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}