{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T12:55:07Z","timestamp":1777640107623,"version":"3.51.4"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,8,3]],"date-time":"2014-08-03T00:00:00Z","timestamp":1407024000000},"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\/s11590-014-0772-4","type":"journal-article","created":{"date-parts":[[2014,8,2]],"date-time":"2014-08-02T21:52:18Z","timestamp":1407016338000},"page":"237-246","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Advantages of simplicial partitioning for Lipschitz optimization problems with linear constraints"],"prefix":"10.1007","volume":"10","author":[{"given":"Remigijus","family":"Paulavi\u010dius","sequence":"first","affiliation":[]},{"given":"Julius","family":"\u017dilinskas","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,8,3]]},"reference":[{"key":"772_CR1","unstructured":"Baker, C.A., Watson, L.T., Grossman, B., Mason, W.H., Haftka, R.T.: Parallel global aircraft configuration design space exploration. In: Tentner A. (ed.) High Performance Computing Symposium 2000, pp. 54\u201366. Society for Computer Simulation International (2000)"},{"issue":"3","key":"772_CR2","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1023\/A:1013729320435","volume":"21","author":"MC Bartholomew-Biggs","year":"2002","unstructured":"Bartholomew-Biggs, M.C., Parkhurst, S.C., Wilson, S.P.: Using DIRECT to solve an aircraft routing problem. Comput. Optim. Appl. 21(3), 311\u2013323 (2002). doi: 10.1023\/A:1013729320435","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"772_CR3","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1023\/A:1013123110266","volume":"2","author":"RG Carter","year":"2001","unstructured":"Carter, R.G., Gablonsky, J.M., Patrick, A., Kelley, C.T., Eslinger, O.J.: Algorithms for noisy problems in gas transmission pipeline optimization. Optim. Eng. 2(2), 139\u2013157 (2001). doi: 10.1023\/A:1013123110266","journal-title":"Optim. Eng."},{"issue":"2","key":"772_CR4","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1016\/j.amc.2005.11.127","volume":"179","author":"L Chiter","year":"2006","unstructured":"Chiter, L.: DIRECT algorithm: a new definition of potentially optimal hyperrectangles. Appl. Math. Comput. 179(2), 742\u2013749 (2006). doi: 10.1016\/j.amc.2005.11.127","journal-title":"Appl. Math. Comput."},{"key":"772_CR5","doi-asserted-by":"crossref","unstructured":"Conn, A.R., Scheinberg, K., Vicente, L.N.: Introduction to derivative-free optimization, vol. 8, SIAM (2009). doi: 10.1137\/1.9780898718768","DOI":"10.1137\/1.9780898718768"},{"issue":"4","key":"772_CR6","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1023\/A:1012782825166","volume":"21","author":"SE Cox","year":"2001","unstructured":"Cox, S.E., Haftka, R.T., Baker, C.A., Grossman, B., Mason, W.H., Watson, L.T.: A comparison of global optimization methods for the design of a high-speed civil transport. J. Global Optim. 21(4), 415\u2013432 (2001). doi: 10.1023\/A:1012782825166","journal-title":"J. Global Optim."},{"key":"772_CR7","doi-asserted-by":"crossref","unstructured":"De Berg, M., Van Kreveld, M., Overmars, M., Schwarzkopf, O.C.: Computational geometry. Springer, Berlin, Heidelberg (2000). doi: 10.1007\/978-3-662-04245-8_1","DOI":"10.1007\/978-3-662-04245-8_1"},{"issue":"793\u2014-800","key":"772_CR8","first-page":"1","volume":"7","author":"B Delaunay","year":"1934","unstructured":"Delaunay, B.: Sur la sphere vide. Izv. Akad. Nauk SSSR. Otdelenie Matematicheskii i Estestvennyka Nauk 7(793\u2014-800), 1\u20132 (1934)","journal-title":"Otdelenie Matematicheskii i Estestvennyka Nauk"},{"issue":"1","key":"772_CR9","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s10957-011-9856-9","volume":"151","author":"D Serafino Di","year":"2011","unstructured":"Di Serafino, D., Liuzzi, G., Piccialli, V., Riccio, F., Toraldo, G.: A modified DIviding RECTangles algorithm for a problem in astrophysics. J. Optim. Theory Appl. 151(1), 175\u2013190 (2011). doi: 10.1007\/s10957-011-9856-9","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"772_CR10","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1007\/s11590-012-0452-1","volume":"7","author":"Y Evtushenko","year":"2013","unstructured":"Evtushenko, Y., Posypkin, M.: A deterministic approach to global box-constrained optimization. Optim. Lett. 7(4), 819\u2013829 (2013)","journal-title":"Optim. Lett."},{"issue":"6","key":"772_CR11","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/0041-5553(71)90065-6","volume":"11","author":"YG Evtushenko","year":"1971","unstructured":"Evtushenko, Y.G.: Numerical methods for finding global extrema (case of a non-uniform mesh). USSR Comput. Math. Math. Phys. 11(6), 38\u201354 (1971)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"772_CR12","unstructured":"Finkel, D.E.: Direct optimization algorithm user guide. Center for Research in Scientific Computation, North Carolina State University 2 (2003)"},{"key":"772_CR13","unstructured":"Finkel, D.E.: Global optimization with the Direct algorithm. Ph.D. thesis, North Carolina State University (2005)"},{"issue":"4","key":"772_CR14","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s10898-006-9029-9","volume":"36","author":"DE Finkel","year":"2006","unstructured":"Finkel, D.E., Kelley, C.T.: Additive scaling and the DIRECT algorithm. J. Global Optim. 36(4), 597\u2013608 (2006). doi: 10.1007\/s10898-006-9029-9","journal-title":"J. Global Optim."},{"key":"772_CR15","volume-title":"Practical Methods of Optimization","author":"R Fletcher","year":"1987","unstructured":"Fletcher, R.: Practical Methods of Optimization, vol. 37. Wiley, New York (1987)"},{"key":"772_CR16","unstructured":"Gablonsky, J.M.: Modifications of the Direct algorithm. Ph.D. thesis, North Carolina State University (2001)"},{"issue":"1","key":"772_CR17","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1023\/A:1017930332101","volume":"21","author":"JM Gablonsky","year":"2001","unstructured":"Gablonsky, J.M., Kelley, C.T.: A locally-biased form of the DIRECT algorithm. J. Global Optim. 21(1), 27\u201337 (2001). doi: 10.1023\/A:1017930332101","journal-title":"J. Global Optim."},{"issue":"1","key":"772_CR18","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1019992822938","volume":"23","author":"J He","year":"2002","unstructured":"He, J., Watson, L.T., Ramakrishnan, N., Shaffer, C.A., Verstak, A., Jiang, J., Bae, K., Tranter, W.H.: Dynamic data structures for a DIRECT search algorithm. Comput. Optim. Appl. 23(1), 5\u201325 (2002). doi: 10.1023\/A:1019992822938","journal-title":"Comput. Optim. Appl."},{"key":"772_CR19","doi-asserted-by":"crossref","unstructured":"Hendrix, E.M., Casado, L.G., Amaral, P.: Global optimization simplex bisection revisited based on considerations by reiner horst. Computational Science and Its Applications-ICCSA 2012, pp. 159\u2013173. Springer, Berlin, Heidelberg (2012). doi: 10.1007\/978-3-642-31137-6_12","DOI":"10.1007\/978-3-642-31137-6_12"},{"key":"772_CR20","volume-title":"Handbook of Global Optimization","year":"1995","unstructured":"Horst, R., Pardalos, P.M. (eds.): Handbook of Global Optimization, vol. 1. Kluwer Academic Publishers, Dordrecht (1995)"},{"key":"772_CR21","volume-title":"Introduction to Global Optimization","author":"R Horst","year":"1995","unstructured":"Horst, R., Pardalos, P.M., Thoai, N.V.: Introduction to Global Optimization. Kluwer Academic Publishers, Nonconvex Optimization and Its Application (1995)"},{"key":"772_CR22","doi-asserted-by":"crossref","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)"},{"issue":"4","key":"772_CR23","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 multilevel coordinate search. J. Global Optim. 14(4), 331\u2013355 (1999)","journal-title":"J. Global Optim."},{"issue":"1","key":"772_CR24","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, B.E.: Lipschitzian optimization without the Lipschitz constant. J. Optim. Theory Appl. 79(1), 157\u2013181 (1993). doi: 10.1007\/BF00941892","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"772_CR25","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s11590-008-0110-9","volume":"3","author":"DE Kvasov","year":"2009","unstructured":"Kvasov, D.E., Sergeyev, Y.D.: A univariate global search working with a set of Lipschitz constants for the first derivative. Optim. Lett. 3(2), 303\u2013318 (2009). doi: 10.1007\/s11590-008-0110-9","journal-title":"Optim. Lett."},{"issue":"16","key":"772_CR26","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). doi: 10.1016\/j.cam.2012.02.020","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"772_CR27","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). doi: 10.1137\/110859129","journal-title":"SIAM J. Optim."},{"issue":"2","key":"772_CR28","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/s10589-008-9217-2","volume":"45","author":"G Liuzzi","year":"2010","unstructured":"Liuzzi, G., Lucidi, S., Piccialli, V.: A direct-based approach exploiting local minimizations for the solution for large-scale global optimization problems. Comput. Optim. Appl. 45(2), 353\u2013375 (2010). doi: 10.1007\/s10589-008-9217-2","journal-title":"Comput. Optim. Appl."},{"issue":"1","key":"772_CR29","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., Piccialli, V.: A partition-based global optimization algorithm. J. Global Optim. 48(1), 113\u2013128 (2010). doi: 10.1007\/s10898-009-9515-y","journal-title":"J. Global Optim."},{"issue":"2","key":"772_CR30","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/BF02592948","volume":"39","author":"KG Murty","year":"1987","unstructured":"Murty, K.G., Kabadi, S.N.: Some NP-complete problems in quadratic and nonlinear programming. Math. Program. 39(2), 117\u2013129 (1987)","journal-title":"Math. Program."},{"key":"772_CR31","unstructured":"Neumaier, A.: MCS: global optimization by multilevel coordinate search. http:\/\/www.mat.univie.ac.at\/neum\/software\/mcs\/"},{"issue":"1","key":"772_CR32","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/0167-6377(88)90049-1","volume":"7","author":"PM Pardalos","year":"1988","unstructured":"Pardalos, P.M., Schnitger, G.: Checking local optimality in constrained quadratic programming is NP-hard. Oper. Res. Lett. 7(1), 33\u201335 (1988)","journal-title":"Oper. Res. Lett."},{"issue":"2\u20133","key":"772_CR33","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1007\/s10898-014-0180-4","volume":"59","author":"R Paulavi\u010dius","year":"2014","unstructured":"Paulavi\u010dius, R., Sergeyev, Y.D., Kvasov, D.E., \u017dilinskas, J.: Globally-biased Disimpl algorithm for expensive global optimization. J. Global Optim. 59(2\u20133), 545\u2013567 (2014). doi: 10.1007\/s10898-014-0180-4","journal-title":"J. Global Optim."},{"issue":"4","key":"772_CR34","first-page":"383","volume":"36","author":"R Paulavi\u010dius","year":"2007","unstructured":"Paulavi\u010dius, R., \u017dilinskas, J.: Analysis of different norms and corresponding Lipschitz constants for global optimization in multidimensional case. Inf. Technol. Control 36(4), 383\u2013387 (2007)","journal-title":"Inf. Technol. Control"},{"issue":"1","key":"772_CR35","doi-asserted-by":"crossref","first-page":"54","DOI":"10.3846\/20294913.2012.661170","volume":"18","author":"R Paulavi\u010dius","year":"2012","unstructured":"Paulavi\u010dius, R., \u017dilinskas, J.: Influence of Lipschitz bounds on the speed of global optimization. Technol. Econ. Dev. Econ. 18(1), 54\u201366 (2012). doi: 10.3846\/20294913.2012.661170","journal-title":"Technol. Econ. Dev. Econ."},{"key":"772_CR36","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-9093-7","volume-title":"Simplicial Global Optimization. SpringerBriefs in Optimization","author":"R Paulavi\u010dius","year":"2014","unstructured":"Paulavi\u010dius, R., \u017dilinskas, J.: Simplicial Global Optimization. SpringerBriefs in Optimization. Springer, New York (2014). doi: 10.1007\/978-1-4614-9093-7"},{"issue":"1","key":"772_CR37","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s10898-013-0089-3","volume":"59","author":"R Paulavi\u010dius","year":"2014","unstructured":"Paulavi\u010dius, R., \u017dilinskas, J.: Simplicial Lipschitz optimization without the Lipschitz constant. J. Global Optim. 59(1), 23\u201340 (2014). doi: 10.1007\/s10898-013-0089-3","journal-title":"J. Global Optim."},{"issue":"2","key":"772_CR38","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 partitions and combination of Lipschitz bounds. Optim. Lett. 4(2), 173\u2013183 (2010). doi: 10.1007\/s11590-009-0156-3","journal-title":"Optim. Lett."},{"key":"772_CR39","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2502-5","volume-title":"Global Optimization in Action (Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications)","author":"JD Pint\u00e9r","year":"1996","unstructured":"Pint\u00e9r, J.D.: Global Optimization in Action (Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications). Kluwer Academic Publishers, Dordrecht (1996)"},{"issue":"4","key":"772_CR40","first-page":"888","volume":"12","author":"SA Piyavskii","year":"1972","unstructured":"Piyavskii, S.A.: An algorithm for finding the absolute extremum of a function. Zh. Vychisl. Mat. mat. Fiz 12(4), 888\u2013896 (1972)","journal-title":"Zh. Vychisl. Mat. mat. Fiz"},{"key":"772_CR41","doi-asserted-by":"crossref","unstructured":"Rios, L.M., Sahinidis, N.V.: Derivative-free optimization: a review of algorithms and comparison of software implementations. J. Global Optim. 56(3), 1247\u20131293 (2012). doi: 10.1007\/s10898-012-9951-y","DOI":"10.1007\/s10898-012-9951-y"},{"issue":"3","key":"772_CR42","doi-asserted-by":"crossref","first-page":"910","DOI":"10.1137\/040621132","volume":"16","author":"YD Sergeyev","year":"2006","unstructured":"Sergeyev, Y.D., Kvasov, D.E.: Global search based on efficient diagonal partitions and a set of Lipschitz constants. SIAM J. Optim. 16(3), 910\u2013937 (2006). doi: 10.1137\/040621132","journal-title":"SIAM J. Optim."},{"key":"772_CR43","first-page":"2812","volume-title":"Wiley Encyclopedia of Operations Research and Management Science (in 8 volumes)","author":"YD Sergeyev","year":"2011","unstructured":"Sergeyev, Y.D., Kvasov, D.E.: Lipschitz global optimization. In: Cochran, J.J., Cox, L.A., Keskinocak, P., Kharoufeh, J.P., Smith, J.C. (eds.) Wiley Encyclopedia of Operations Research and Management Science (in 8 volumes), vol. 4, pp. 2812\u20132828. Wiley, New York (2011)"},{"issue":"3","key":"772_CR44","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s10107-003-0372-z","volume":"96","author":"YD Sergeyev","year":"2003","unstructured":"Sergeyev, Y.D., Pugliese, P., Famularo, D.: Index information algorithm with local tuning for solving multidimensional global optimization problems with multiextremal constraints. Math. Program. 96(3), 489\u2013512 (2003). doi: 10.1007\/s10107-003-0372-z","journal-title":"Math. Program."},{"key":"772_CR45","unstructured":"Vaz, A.I.F.: PSwarm solver home page (2010). http:\/\/www.norg.uminho.pt\/aivaz\/pswarm\/ . Accessed 12 Dec 2013"},{"issue":"4\u20135","key":"772_CR46","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1080\/10556780902909948","volume":"24","author":"AIF Vaz","year":"2009","unstructured":"Vaz, A.I.F., Vicente, L.: Pswarm: a hybrid solver for linearly constrained global derivative-free optimization. Optim. Methods Softw. 24(4\u20135), 669\u2013685 (2009)","journal-title":"Optim. Methods Softw."},{"issue":"1","key":"772_CR47","doi-asserted-by":"crossref","first-page":"145","DOI":"10.3846\/1392-6292.2008.13.145-159","volume":"13","author":"J \u017dilinskas","year":"2008","unstructured":"\u017dilinskas, J.: Branch and bound with simplicial partitions for global optimization. Math. Model. Anal. 13(1), 145\u2013159 (2008). doi: 10.3846\/1392-6292.2008.13.145-159","journal-title":"Math. Model. Anal."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-014-0772-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-014-0772-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-014-0772-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T17:11:39Z","timestamp":1559409099000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-014-0772-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8,3]]},"references-count":47,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,2]]}},"alternative-id":["772"],"URL":"https:\/\/doi.org\/10.1007\/s11590-014-0772-4","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8,3]]}}}