{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T09:50:21Z","timestamp":1742637021623},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,3,15]],"date-time":"2014-03-15T00:00:00Z","timestamp":1394841600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2014,11]]},"DOI":"10.1007\/s10957-014-0531-9","type":"journal-article","created":{"date-parts":[[2014,3,18]],"date-time":"2014-03-18T05:57:56Z","timestamp":1395122276000},"page":"528-547","source":"Crossref","is-referenced-by-count":6,"title":["On a Global Optimization Algorithm for Bivariate Smooth Functions"],"prefix":"10.1007","volume":"163","author":[{"given":"James M.","family":"Calvin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antanas","family":"\u017dilinskas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,3,15]]},"reference":[{"key":"531_CR1","doi-asserted-by":"crossref","unstructured":"Mockus, J.: Bayesian Approach to Global Optimization. Kluwer Academic Publishers, Dordrecht (1988)","DOI":"10.1007\/978-94-009-0909-0_7"},{"key":"531_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/3-540-50871-6_1","volume":"350","author":"A T\u00f6rn","year":"1989","unstructured":"T\u00f6rn, A., \u017dilinskas, A.: Global optimization. Lect. Notes Comput. Sci. 350, 1\u2013255 (1989)","journal-title":"Lect. Notes Comput. Sci."},{"key":"531_CR3","doi-asserted-by":"crossref","unstructured":"Strongin, R., Sergeyev, Y.: Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht (2000)","DOI":"10.1007\/978-1-4615-4677-1"},{"key":"531_CR4","unstructured":"Zhigljavsy, A., \u017dilinskas, A.: Stochastic Global Optimization. Springer, New York (2008)"},{"key":"531_CR5","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1023\/A:1004699313526","volume":"106","author":"JM Calvin","year":"2000","unstructured":"Calvin, J.M., \u017dilinskas, A.: A one-dimensional P-algorithm with convergence rate $$O(n^{-3+\\delta })$$ O ( n - 3 + \u03b4 ) for smooth functions. J. Optim. Theory Appl. 106, 297\u2013307 (2000)","journal-title":"J. Optim. Theory Appl."},{"key":"531_CR6","unstructured":"Calvin, J.M., Chen, Y., \u017dilinskas, A.: An adaptive univariate global optimization algorithm and its convergence rate for twice continuously differentiable functions. J. Optim. Theory Appl. 155, 628\u2013636 (2012)"},{"key":"531_CR7","unstructured":"Horst, R., Pardalos, P., Thoai, N.: Introduction to Global Optimization. Kluwer Academic Publishers, Dordrecht (1995)"},{"key":"531_CR8","doi-asserted-by":"crossref","unstructured":"Scholz, D.: Deterministic Global Optimization: Geometric Branch-and-Bound Methods and their Applications. Springer, New York (2012)","DOI":"10.1007\/978-1-4614-1951-8"},{"key":"531_CR9","unstructured":"Sergeyev, Y., Kvasov, D.: Diagonal Global Optimization Methods (in Russian). Fizmatlit, Moscow (2008)"},{"key":"531_CR10","doi-asserted-by":"crossref","unstructured":"Pinter, J.: Global Optimization in Action. Kluwer Academic Publisher, Dordrecht (1996)","DOI":"10.1007\/978-1-4757-2502-5"},{"key":"531_CR11","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF00941892","volume":"79","author":"DR Jones","year":"1993","unstructured":"Jones, D.R., Perttunen, C.D., Stuckman, C.D.: Lipschitzian optimization without the Lipschitz constant. J. Optim. Theory Appl. 79, 157\u2013181 (1993)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"531_CR12","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01096738","volume":"3","author":"W Baritompa","year":"1993","unstructured":"Baritompa, W.: Customizing methods for global optimization: a geometric viewpoint. J. Glob. Opt. 3(2), 193\u2013212 (1993)","journal-title":"J. Glob. Opt."},{"key":"531_CR13","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1016\/S0898-1221(02)00205-5","volume":"44","author":"J Clausen","year":"2002","unstructured":"Clausen, J., \u017dilinskas, A.: Global optimization by means of branch and bound with simplex based covering. Comput. Math. Appl. 44, 943\u2013995 (2002)","journal-title":"Comput. Math. Appl."},{"key":"531_CR14","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1023\/A:1008382309369","volume":"14","author":"W Huyer","year":"1999","unstructured":"Huyer, W., Neumaier, A.: Global optimization by multi-level coordinate search. J. Glob. Opt. 14, 331\u2013355 (1999)","journal-title":"J. Glob. Opt."},{"issue":"16","key":"531_CR15","doi-asserted-by":"crossref","first-page":"4042","DOI":"10.1016\/j.cam.2012.02.020","volume":"236","author":"D Kvasov","year":"2012","unstructured":"Kvasov, D., Sergeyev, Y.: 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":"531_CR16","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s10898-009-9515-y","volume":"48","author":"G Liuzzi","year":"2010","unstructured":"Liuzzi, G., Lucidi, S., Picciali, V.: A partition-based global optimization algorithm. J. Glob. Opt. 48(1), 113\u2013128 (2010)","journal-title":"J. Glob. Opt."},{"key":"531_CR17","doi-asserted-by":"crossref","unstructured":"Sergeyev, Y., Strongin, R., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer, New York (2013)","DOI":"10.1007\/978-1-4614-8042-6"},{"key":"531_CR18","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1007\/0-306-48332-7_41","volume-title":"Encyclopedia of Optimization","author":"G Wood","year":"2001","unstructured":"Wood, G.: Bisection global optimization methods. In: Floudas, C., Pardalos, P. (eds.) Encyclopedia of Optimization, pp. 186\u2013189. Kluwer Academic Publisher, Dordrecht (2001)"},{"key":"531_CR19","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1016\/S0898-1221(02)00206-7","volume":"44","author":"A \u017dilinskas","year":"2002","unstructured":"\u017dilinskas, A., \u017dilinskas, J.: Global optimization based on a statistical model and simplicial partitioning. Comput. Math. Appl. 44, 957\u2013967 (2002)","journal-title":"Comput. Math. Appl."},{"key":"531_CR20","doi-asserted-by":"crossref","first-page":"451","DOI":"10.3846\/13926292.2011.602988","volume":"16","author":"A \u017dilinskas","year":"2011","unstructured":"\u017dilinskas, A., \u017dilinskas, J.: A global optimization method based on the reduced simplicial statistical model. Math. Model. Anal. 16, 451\u2013460 (2011)","journal-title":"Math. Model. Anal."},{"key":"531_CR21","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s11590-009-0156-3","volume":"4","author":"R Paulavi\u010dius","year":"2010","unstructured":"Paulavi\u010dius, R., \u017dilinskas, J., Grothey, A.: Investigation of selection strategies in branch and bound algorithm with simplicial partition and combination of Lipschitz bounds. Optim. Lett. 4, 173\u2013183 (2010)","journal-title":"Optim. Lett."},{"issue":"3","key":"531_CR22","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1016\/j.ejor.2007.01.056","volume":"191","author":"E Hendrix","year":"2008","unstructured":"Hendrix, E., Casado, L., Garcia, I.: The semi-continuous quadratic mixture design problem: description and branch-and-bound approach. Eur. J. Oper. Res. 191(3), 803\u2013815 (2008)","journal-title":"Eur. J. Oper. Res."},{"key":"531_CR23","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.cam.2004.08.005","volume":"177","author":"Y Wu","year":"2005","unstructured":"Wu, Y., Ozdamar, L., Kumar, A.: Triopt: a triangulation-based partitioning algorithm for gloabal optimization. J. Comput. Appl. Math. 177, 35\u201353 (2005)","journal-title":"J. Comput. Appl. Math."},{"key":"531_CR24","doi-asserted-by":"crossref","unstructured":"Fishburn, P.: Utility Theory for Decision Making. Wiley, New York (1970)","DOI":"10.21236\/AD0708563"},{"key":"531_CR25","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1007\/BF01581029","volume":"22","author":"A \u017dilinskas","year":"1982","unstructured":"\u017dilinskas, A.: Axiomatic approach to statistical models and their use in multimodal optimizatio theory. Math. Program. 22, 104\u2013116 (1982)","journal-title":"Math. Program."},{"key":"531_CR26","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/0022-247X(62)90011-2","volume":"5","author":"H Kushner","year":"1962","unstructured":"Kushner, H.: A versatile stochastic model of a function of unknown and time-varying form. J. Math. Anal. Appl. 5, 150\u2013167 (1962)","journal-title":"J. Math. Anal. Appl."},{"key":"531_CR27","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/0167-6377(85)90049-5","volume":"4","author":"A \u017dilinskas","year":"1985","unstructured":"\u017dilinskas, A.: Axiomatic characterization of a global optimization algorithm and investigation of its search strategies. Oper. Res. Lett. 4, 35\u201339 (1985)","journal-title":"Oper. Res. Lett."},{"key":"531_CR28","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/B978-0-12-587260-7.50011-X","volume-title":"Mathematical Software III","author":"C Lawson","year":"1977","unstructured":"Lawson, C.: Software for C1 surface interpolation. In: Rice, J.R. (ed.) Mathematical Software III, vol. 1, pp. 161\u2013194. Academic Press, New York (1977)"},{"key":"531_CR29","unstructured":"Hjelle, \u00d8., D\u00e6len, M.: Triangulations and Applications. Springer-Verlag, New York (2006)"},{"key":"531_CR30","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0925-7721(01)00047-5","volume":"22","author":"JR Shewchuck","year":"2002","unstructured":"Shewchuck, J.R.: Delaunay refinement algorithms for triangular mesh generation. Comput. Geom. 22, 21\u201331 (2002)","journal-title":"Comput. Geom."},{"key":"531_CR31","unstructured":"Cgal, Computational Geometry Algorithms Library. URL http:\/\/www.cgal.org . Accessed 1 Oct 2013"},{"key":"531_CR32","unstructured":"Waldron, S.: Sharp error estimates for multivariate positive linear operators which reproduce the linear polynomials. In: Chui, C.K., Schumaker, L.L. (eds.) Approximation Theory IX, vol. 1, pp. 339\u2013346. Vanderbilt University Press, Nashville (1998)"},{"key":"531_CR33","unstructured":"Rastrigin, L.: Statistical Models of Search (in Russian). Nauka (1968)."},{"issue":"5","key":"531_CR34","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1147\/rd.165.0504","volume":"16","author":"F Branin","year":"1972","unstructured":"Branin, F.: Widely convergent method for finding multiple solutions of simultaneous nonlinear equations. IBM J. Res. Dev. 16(5), 504\u2013522 (1972)","journal-title":"IBM J. Res. Dev."},{"key":"531_CR35","unstructured":"Dixon, L.C.W., Szeg\u00f6, G.P. (eds.): Towards Global Optimization II. North Holland, New York (1978)"},{"key":"531_CR36","unstructured":"DIRECT - A Global Optimization Algorithm. URL http:\/\/www4.ncsu.edu\/ctk\/Finkel.Direct . Accessed 1 Oct 2013"},{"key":"531_CR37","doi-asserted-by":"crossref","unstructured":"Hansen, P., Jaumard, B.: Lipshitz optimization. In: Horst, R., Pardalos, P. (eds.) Handbook of Global Optimization, pp. 407\u2013493. Kluwer Academic Publisher, Dodrecht (1995)","DOI":"10.1007\/978-1-4615-2025-2_9"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-014-0531-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-014-0531-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-014-0531-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T03:11:36Z","timestamp":1648609896000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-014-0531-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,15]]},"references-count":37,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,11]]}},"alternative-id":["531"],"URL":"https:\/\/doi.org\/10.1007\/s10957-014-0531-9","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,3,15]]}}}