{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:59:42Z","timestamp":1760889582209,"version":"3.37.3"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,3,7]],"date-time":"2018-03-07T00:00:00Z","timestamp":1520380800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,3,7]],"date-time":"2018-03-07T00:00:00Z","timestamp":1520380800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004504","name":"Lietuvos Mokslo Taryba","doi-asserted-by":"publisher","award":["P-MIP-17-61"],"award-info":[{"award-number":["P-MIP-17-61"]}],"id":[{"id":"10.13039\/501100004504","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CMMI-0926949"],"award-info":[{"award-number":["CMMI-0926949"]}],"id":[{"id":"10.13039\/100000001","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":[[2018,5]]},"DOI":"10.1007\/s10898-018-0636-z","type":"journal-article","created":{"date-parts":[[2018,3,7]],"date-time":"2018-03-07T04:29:20Z","timestamp":1520396960000},"page":"165-191","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["On convergence rate of a rectangular partition based global optimization algorithm"],"prefix":"10.1007","volume":"71","author":[{"given":"James","family":"Calvin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gra\u017eina","family":"Gimbutien\u0117","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"William O.","family":"Phillips","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3091-0569","authenticated-orcid":false,"given":"Antanas","family":"\u017dilinskas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,7]]},"reference":[{"key":"636_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4949-6","volume-title":"Deterministic Global Optimization: Theory, Algorithms and Applications","author":"Ch Floudas","year":"2000","unstructured":"Floudas, Ch.: Deterministic Global Optimization: Theory, Algorithms and Applications. Kluwer, Dordrecht (2000)"},{"key":"636_CR2","volume-title":"Introduction to Global Optimization","author":"R Horst","year":"1995","unstructured":"Horst, R., Pardalos, A.P., Thoai, N.: Introduction to Global Optimization. Kluwer, Dordrecht (1995)"},{"key":"636_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03199-5","volume-title":"Global Optimization: Deterministic Approaches","author":"R Horst","year":"1996","unstructured":"Horst, R., Tuy, H.: Global Optimization: Deterministic Approaches. Springer, Berlin (1996)"},{"key":"636_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2502-5","volume-title":"Global Optimization in Action","author":"J Pinter","year":"1996","unstructured":"Pinter, J.: Global Optimization in Action. Kluwer, Dordrecht (1996)"},{"issue":"5","key":"636_CR5","first-page":"743","volume":"39","author":"YD Sergeyev","year":"1999","unstructured":"Sergeyev, Y.D.: Multidimensional global optimization using the first derivatives. Comput. Maths. Math. Phys. 39(5), 743\u2013752 (1999)","journal-title":"Comput. Maths. Math. Phys."},{"key":"636_CR6","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/j.cnsns.2014.08.026","volume":"21","author":"YD Sergeyev","year":"2015","unstructured":"Sergeyev, Y.D., Kvasov, D.E.: A deterministic global optimization using smooth diagonal auxiliary functions. Commun. Nonlinear Sci. Numer. Simul. 21, 99\u2013111 (2015)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"636_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-7199-2","volume-title":"Deterministic Global Optimization, An Introduction to the Diagonal Approach","author":"YD Sergeyev","year":"2017","unstructured":"Sergeyev, Y.D., Kvasov, D.E.: Deterministic Global Optimization, An Introduction to the Diagonal Approach. Springer, New York (2017)"},{"key":"636_CR8","volume-title":"Bayesian Approach to Global Optimization","author":"J Mockus","year":"1988","unstructured":"Mockus, J.: Bayesian Approach to Global Optimization. Kluwer, Dordrecht (1988)"},{"key":"636_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-4677-1","volume-title":"Global Optimization with Non-convex Constraints: Sequential and Parallel Algorithms","author":"RG Strongin","year":"2000","unstructured":"Strongin, R.G., Sergeyev, Y.D.: Global Optimization with Non-convex Constraints: Sequential and Parallel Algorithms. Kluwer, Dordrecht (2000)"},{"key":"636_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3436-1","volume-title":"Theory of Global Random Search","author":"A Zhigljavsky","year":"1991","unstructured":"Zhigljavsky, A.: Theory of Global Random Search. Kluwer, Dordrecht (1991)"},{"issue":"1","key":"636_CR11","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1080\/00207721.2012.702244","volume":"45","author":"A \u017dilinskas","year":"2014","unstructured":"\u017dilinskas, A.: A statistical model-based algorithm for black-box multi-objective optimisation. Int. J. Syst. Sci. 45(1), 82\u201392 (2014)","journal-title":"Int. J. Syst. Sci."},{"key":"636_CR12","doi-asserted-by":"publisher","first-page":"229","DOI":"10.15388\/Informatica.2016.83","volume":"27","author":"A \u017dilinskas","year":"2016","unstructured":"\u017dilinskas, A., Zhigljavsy, A.: Stochastic global optimization: a review on the occasion of 25 years of Informatica. Informatica 27, 229\u2013256 (2016)","journal-title":"Informatica"},{"key":"636_CR13","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/BF02430364","volume":"11","author":"J Hooker","year":"1995","unstructured":"Hooker, J.: Testing heuristics: we have it all wrong. J. Heuristics 11, 33\u201342 (1995)","journal-title":"J. Heuristics"},{"key":"636_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-5362-2","volume-title":"Handbook of Global Optimization","author":"P Pardalos","year":"2002","unstructured":"Pardalos, P., Romeijn, H.: Handbook of Global Optimization, vol. 2. Springer, Berlin (2002)"},{"key":"636_CR15","unstructured":"Rastrigin, L.: Statistical Models of Search. Nauka (2013) (in Russian)"},{"key":"636_CR16","first-page":"545567","volume":"59","author":"R Paulavi\u010dius","year":"2014","unstructured":"Paulavi\u010dius, R., Sergeyev, Y., Kvasov, D., Z\u0306ilinskas, J.: Globally-biased DISIMPL algorithm for expensive global optimization. J. Glob. Optim. 59, 545567 (2014)","journal-title":"J. Glob. Optim."},{"key":"636_CR17","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1007\/s10898-011-9840-9","volume":"56","author":"A \u017dilinskas","year":"2013","unstructured":"\u017dilinskas, A., Z\u0306ilinskas, J.: A hybrid global optimization algorithm for non-linear leist squares regression. J. Glob. Optim. 56, 265\u2013277 (2013)","journal-title":"J. Glob. Optim."},{"key":"636_CR18","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1023\/A:1004699313526","volume":"106","author":"J Calvin","year":"2000","unstructured":"Calvin, J., \u017dilinskas, A.: A one-dimensional P-algorithm with convergence rate $$o(n^{-3+\\delta })$$ for smooth functions. J. Optim. Theory Appl. 106, 297\u2013307 (2000)","journal-title":"J. Optim. Theory Appl."},{"key":"636_CR19","doi-asserted-by":"crossref","first-page":"471","DOI":"10.15388\/Informatica.2011.337","volume":"22","author":"JM Calvin","year":"2010","unstructured":"Calvin, J.M.: An adaptive univariate global optimization algorithm and its convergence rate under the Wiener measure. Informatica 22, 471\u2013488 (2010)","journal-title":"Informatica"},{"key":"636_CR20","doi-asserted-by":"publisher","first-page":"628","DOI":"10.1007\/s10957-012-0060-3","volume":"155","author":"JM Calvin","year":"2011","unstructured":"Calvin, J.M., Chen, Y., Z\u0306ilinskas, A.: An adaptive univariate global optimization algorithm and its convergence rate for twice continuously differentiable functions. J. Optim. Theory Appl. 155, 628\u2013636 (2011)","journal-title":"J. Optim. Theory Appl."},{"key":"636_CR21","doi-asserted-by":"publisher","first-page":"528","DOI":"10.1007\/s10957-014-0531-9","volume":"163","author":"JM Calvin","year":"2014","unstructured":"Calvin, J.M., Z\u0306ilinskas, A.: On a global optimization of bivariate smooth functions. J. Optim. Theory Appl. 163, 528\u2013547 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"636_CR22","doi-asserted-by":"publisher","DOI":"10.4171\/084","volume-title":"Tractability of Multivariate Problems, II. Tracts in Mathematics","author":"E Novak","year":"2010","unstructured":"Novak, E., Wo\u017aniakowski, H.: Tractability of Multivariate Problems, II. Tracts in Mathematics, vol. 12. European Mathematical Society, Z\u00fcrich (2010)"},{"key":"636_CR23","doi-asserted-by":"publisher","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. Optim. 14, 331\u2013355 (1999)","journal-title":"J. Glob. Optim."},{"key":"636_CR24","doi-asserted-by":"publisher","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":"3","key":"636_CR25","doi-asserted-by":"publisher","first-page":"910","DOI":"10.1137\/040621132","volume":"16","author":"Y Sergeyev","year":"2006","unstructured":"Sergeyev, Y., Kvasov, D.: Global search based on efficicient diagonal partitions and set of Lipschitz constants. SIAM J. Optim. 16(3), 910\u2013937 (2006)","journal-title":"SIAM J. Optim."},{"key":"636_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-1951-8","volume-title":"Deterministic Global Optimization: Geometric Branch-and-Bound Methods and their Applications","author":"D Scholz","year":"2012","unstructured":"Scholz, D.: Deterministic Global Optimization: Geometric Branch-and-Bound Methods and their Applications. Springer, Berlin (2012)"},{"key":"636_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-9093-7","volume-title":"Simplicial Global Optimization. Springer Briefs in Optimization","author":"R Paulavi\u010dius","year":"2014","unstructured":"Paulavi\u010dius, R., Z\u0306ilinskas, J.: Simplicial Global Optimization. Springer Briefs in Optimization. Springer, Berlin (2014)"},{"key":"636_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0079792","volume-title":"Deterministic and Stochastic Error Bounds in Numerical Analysis, Lecture Notes in Mathematics","author":"E Novak","year":"1988","unstructured":"Novak, E.: Deterministic and Stochastic Error Bounds in Numerical Analysis, Lecture Notes in Mathematics, vol. 1349. Springer, Berlin (1988)"},{"key":"636_CR29","volume-title":"Stochastic Global Optimization","author":"A Zhigljavsy","year":"2008","unstructured":"Zhigljavsy, A., \u017dilinskas, A.: Stochastic Global Optimization. Springer, Berlin (2008)"},{"key":"636_CR30","first-page":"339","volume-title":"Approximation Theory IX","author":"S Waldron","year":"1998","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":"636_CR31","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/978-1-4757-5362-2_14","volume-title":"Handbook of Global Optimization","author":"C McGeoch","year":"2002","unstructured":"McGeoch, C.: Experimental analysis of algorithms. In: Pardalos, P., Romeijn, E. (eds.) Handbook of Global Optimization, vol. 2, pp. 489\u2013514. Kluwer, Dodrecht (2002)"},{"key":"636_CR32","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1137\/080724083","volume":"20","author":"J More","year":"2009","unstructured":"More, J., Wild, S.: Benchmarking derivative-free optimization algorithms. SIAM J. Optim. 20, 172\u2013191 (2009)","journal-title":"SIAM J. Optim."},{"key":"636_CR33","unstructured":"GSL, GNU Scientific Library. \n                    https:\/\/www.gnu.org\/software\/gsl\/\n                    \n                  . Accessed on 1 Aug 2016"},{"key":"636_CR34","unstructured":"Cgal, Computational Geometry Algorithms Library. \n                    http:\/\/www.cgal.org\n                    \n                  . Accessed on 15 Oct 2014"},{"key":"636_CR35","first-page":"790793","volume":"16","author":"I Sobol","year":"1979","unstructured":"Sobol, I.: On the systematic search in a hypercube. SIAM J. Numer. Anal. 16, 790793 (1979)","journal-title":"SIAM J. Numer. Anal."},{"volume-title":"Towards Global Optimization II","year":"1978","key":"636_CR36","unstructured":"Dixon, L.C.W., Szeg\u00f6, G.P. (eds.): Towards Global Optimization II. North Holland, New York (1978)"},{"issue":"5","key":"636_CR37","doi-asserted-by":"publisher","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":"636_CR38","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1007\/978-1-4615-2025-2_9","volume-title":"Handbook of Global Optimization","author":"P Hansen","year":"1995","unstructured":"Hansen, P., Jaumard, B.: Lipshitz optimization. In: Horst, R., Pardalos, P. (eds.) Handbook of Global Optimization, pp. 407\u2013493. Kluwer, Dodrecht (1995)"},{"key":"636_CR39","doi-asserted-by":"publisher","first-page":"229251","DOI":"10.1007\/s10898-015-0283-6","volume":"63","author":"H Liu","year":"2015","unstructured":"Liu, H., Xu, S., Ma, Y., Wang, X.: Global optimization of expensive black box functions using potential lipschitz constants and response surfaces. J. Glob. Optim. 63, 229251 (2015)","journal-title":"J. Glob. Optim."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-018-0636-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-0636-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-018-0636-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T07:27:49Z","timestamp":1589700469000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-018-0636-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,7]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,5]]}},"alternative-id":["636"],"URL":"https:\/\/doi.org\/10.1007\/s10898-018-0636-z","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"type":"print","value":"0925-5001"},{"type":"electronic","value":"1573-2916"}],"subject":[],"published":{"date-parts":[[2018,3,7]]},"assertion":[{"value":"4 October 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 February 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}