{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:43:39Z","timestamp":1775054619870,"version":"3.50.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,7,12]],"date-time":"2015-07-12T00:00:00Z","timestamp":1436659200000},"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":["J Glob Optim"],"published-print":{"date-parts":[[2016,9]]},"DOI":"10.1007\/s10898-015-0319-y","type":"journal-article","created":{"date-parts":[[2015,7,11]],"date-time":"2015-07-11T12:47:25Z","timestamp":1436618845000},"page":"21-34","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["On numerical solving the spherical separability problem"],"prefix":"10.1007","volume":"66","author":[{"given":"M.","family":"Gaudioso","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T. V.","family":"Gruzdeva","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. S.","family":"Strekalovsky","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,7,12]]},"reference":[{"key":"319_CR1","unstructured":"Eremin, I.I.: Theory of linear optimization. Ser. Inverse and Ill-Posed Problems. VSP, Utrecht (2002)"},{"issue":"3","key":"319_CR2","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1287\/opre.13.3.444","volume":"13","author":"OL Mangasarian","year":"1965","unstructured":"Mangasarian, O.L.: Linear and nonlinear separation of patterns by linear programming. Oper. Res. 13(3), 444\u2013452 (1965)","journal-title":"Oper. Res."},{"issue":"2","key":"319_CR3","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1023\/A:1013649822153","volume":"112","author":"A Astorino","year":"2002","unstructured":"Astorino, A., Gaudioso, M.: Polyhedral separability through successive LP. J. Optim. Theory Appl. 112(2), 265\u2013293 (2002)","journal-title":"J. Optim. Theory Appl."},{"key":"319_CR4","unstructured":"Mazurov, V.D., Khachay, MYu., Rybin, A.I.: Committee constructions for solving problems of selection, diagnostics and prediction. In: Proceedings of the Steklov Institute of Mathematics, vol. 1, pp. S67\u2013S101 (2002)"},{"key":"319_CR5","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/0022-247X(65)90150-2","volume":"10","author":"JB Rosen","year":"1965","unstructured":"Rosen, J.B.: Pattern separation by convex programming. J. Math. Anal. Appl. 10, 123\u2013134 (1965)","journal-title":"J. Math. Anal. Appl."},{"key":"319_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2440-0","volume-title":"The nature of the statistical learning theory","author":"V Vapnik","year":"1995","unstructured":"Vapnik, V.: The nature of the statistical learning theory. Springer, New York (1995)"},{"key":"319_CR7","volume-title":"Applications and Algorithms of Complementarity","author":"OL Mangasarian","year":"2000","unstructured":"Mangasarian, O.L., Musicant, D.R.: Data discrimination via nonlinear generalized Support Vector Machines. In: Ferris, M.C., Mangasarian, O.L., Pang, J.S. (eds.) Applications and Algorithms of Complementarity. Kluwer, Dordrecht (2000)"},{"key":"319_CR8","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1007\/s10287-007-0051-2","volume":"6","author":"A Astorino","year":"2009","unstructured":"Astorino, A., Gaudioso, M.: A fixed-center spherical separation algorithm with kernel transformations for classification problems. Comput. Manag. Sci. 6, 357\u2013372 (2009)","journal-title":"Comput. Manag. Sci."},{"key":"319_CR9","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/s10589-012-9486-7","volume":"53","author":"A Astorino","year":"2012","unstructured":"Astorino, A., Fuduli, A., Gaudioso, M.: Margin maximization in spherical separation. Comput. Optim. Appl. 53, 301\u2013322 (2012)","journal-title":"Comput. Optim. Appl."},{"issue":"4","key":"319_CR10","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1007\/s10898-010-9558-0","volume":"48","author":"A Astorino","year":"2010","unstructured":"Astorino, A., Fuduli, A., Gaudioso, M.: DC models for spherical separation. J. Glob. Optim. 48(4), 657\u2013669 (2010)","journal-title":"J. Glob. Optim."},{"key":"319_CR11","first-page":"155","volume":"2","author":"DMJ Tax","year":"2002","unstructured":"Tax, D.M.J., Duin, R.P.W.: Uniform object generation for optimizing one-class classifiers. J. Mach. Learn. Res. 2, 155\u2013173 (2002)","journal-title":"J. Mach. Learn. Res."},{"key":"319_CR12","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-8042-6","volume-title":"Introduction to Global Optimization Exploiting Space-Filling Curves","author":"YaD Sergeyev","year":"2013","unstructured":"Sergeyev, YaD, Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer, New York (2013)"},{"key":"319_CR13","volume-title":"Elements of Nonconvex Optimization (in Russian)","author":"AS Strekalovsky","year":"2003","unstructured":"Strekalovsky, A.S.: Elements of Nonconvex Optimization (in Russian). Nauka Publ, Novosibirsk (2003)"},{"key":"319_CR14","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.amc.2014.08.092","volume":"255","author":"AS Strekalovsky","year":"2015","unstructured":"Strekalovsky, A.S.: On local search in d.c. optimization problems. Appl. Math. Comput. 255, 73\u201383 (2015)","journal-title":"Appl. Math. Comput."},{"key":"319_CR15","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/978-1-4939-0808-0_23","volume-title":"Optimization in Science and Engineering","author":"AS Strekalovsky","year":"2014","unstructured":"Strekalovsky, A.S.: On solving optimization problems with Hidden nonconvex structures. In: Rassias, T.M., Floudas, C.A., Butenko, S. (eds.) Optimization in Science and Engineering, pp. 465\u2013502. Springer, New York (2014)"},{"key":"319_CR16","volume-title":"Introduction to Global Optimization","author":"R Horst","year":"1995","unstructured":"Horst, R., Pardalos, P., Thoai, N.V.: Introduction to Global Optimization. Kluwer, Dordrecht (1995)"},{"key":"319_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12603-5","volume-title":"Nondifferentiable Optimization","author":"VF Demyanov","year":"1985","unstructured":"Demyanov, V.F., Vasiliev, L.V.: Nondifferentiable Optimization. Optimization Software Inc, New York (1985)"},{"key":"319_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-82118-9","volume-title":"Minimization Methods for Non-differentiable Functions","author":"NZ Shor","year":"1985","unstructured":"Shor, N.Z.: Minimization Methods for Non-differentiable Functions. Springer, New York (1985)"},{"key":"319_CR19","volume-title":"Convex Analysis and Extremum Problems (in Russian)","author":"BN Pshenichny","year":"1980","unstructured":"Pshenichny, B.N.: Convex Analysis and Extremum Problems (in Russian). Nauka Publ, Moscow (1980)"},{"issue":"1","key":"319_CR20","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1590\/S0101-82052007000100006","volume":"26","author":"WF Mascarenhas","year":"2007","unstructured":"Mascarenhas, W.F.: On divergence of line search methods. Comput. Appl. Math. 26(1), 129\u2013169 (2007)","journal-title":"Comput. Appl. Math."},{"issue":"1","key":"319_CR21","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/s10107-003-0421-7","volume":"99","author":"WF Mascarenhas","year":"2004","unstructured":"Mascarenhas, W.F.: The BFGS algorithm with exact line searches fails for nonconvex functions. Math. Program. 99(1), 49\u201361 (2004)","journal-title":"Math. Program."},{"key":"319_CR22","unstructured":"Murphy, P.M., Aha, D.W.: UCI repository of machine learning databases. http:\/\/www.ics.uci.edu\/mlearn\/MLRepository.html . Accessed 27 October (2014)"},{"key":"319_CR23","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1086\/116063","volume":"103","author":"S Odewahn","year":"1992","unstructured":"Odewahn, S., Stockwell, E., Pennington, R., Humphreys, R., Zumach, W.: Automated star\/galaxy discrimination with neural networks. Astron. J. 103, 318\u2013331 (1992)","journal-title":"Astron. J."},{"key":"319_CR24","doi-asserted-by":"crossref","unstructured":"Chapelle, O., Zien, A.: Semi-supervised classification by low density separation. Proceedings of the tenth international workshop on artificial intelligence and statistics, pp. 57\u201364 (2005)","DOI":"10.7551\/mitpress\/9780262033589.001.0001"},{"key":"319_CR25","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02796-7","volume-title":"Convex Analysis and Minimization Algorithms","author":"J-B Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty, J.-B., Lemarshal, C.: Convex Analysis and Minimization Algorithms. Springer, Berlin (1993)"},{"key":"319_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/b98874","volume-title":"Numerical optimization","author":"J Nocedal","year":"1999","unstructured":"Nocedal, J., Wright, S.J.: Numerical optimization. Springer, New York (1999)"},{"key":"319_CR27","first-page":"249","volume-title":"Fermat days 85","author":"PD Tao","year":"1986","unstructured":"Tao, P.D., Souad, L.B.: Algorithms for solving a class of non convex optimization. Methods of subgradients. In: Hiriart-Urruty, J.-B. (ed.) Fermat days 85, pp. 249\u2013271. Elservier Sience Publishers B.V, North Holland (1986)"},{"key":"319_CR28","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s10479-004-5022-1","volume":"133","author":"LTH An","year":"2005","unstructured":"An, L.T.H., Tao, P.D.: The DC (difference of convex functions) Programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133, 23\u201346 (2005)","journal-title":"Ann. Oper. Res."},{"issue":"1","key":"319_CR29","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10898-009-9514-z","volume":"48","author":"AS Strekalovsky","year":"2010","unstructured":"Strekalovsky, A.S., Orlov, A.V., Malyshev, A.V.: On computational search for optimistic solutions in bilevel problems. J. Glob. Optim. 48(1), 159\u2013172 (2010)","journal-title":"J. Glob. Optim."},{"issue":"3","key":"319_CR30","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1134\/S0965542507030049","volume":"47","author":"TV Gruzdeva","year":"2007","unstructured":"Gruzdeva, T.V., Strekalovsky, A.S.: Local search in problems with nonconvex constraints. Comput. Math. Math. Phys. 47(3), 381\u2013396 (2007)","journal-title":"Comput. Math. Math. Phys."},{"issue":"3","key":"319_CR31","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1007\/s10898-012-9885-4","volume":"56","author":"TV Gruzdeva","year":"2013","unstructured":"Gruzdeva, T.V.: On a continuous approach for the maximum weighted clique problem. J. Glob. Optim. 56(3), 971\u2013981 (2013)","journal-title":"J. Glob. Optim."},{"issue":"4","key":"319_CR32","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1007\/s10287-013-0193-3","volume":"11","author":"A Astorino","year":"2014","unstructured":"Astorino, A., Gaudioso, M., Khalaf, W.: Edge detection by spherical separation. Comput. Manag. Sci. 11(4), 517\u2013530 (2014)","journal-title":"Comput. Manag. Sci."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-015-0319-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-015-0319-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-015-0319-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T23:49:59Z","timestamp":1652831399000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-015-0319-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,12]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,9]]}},"alternative-id":["319"],"URL":"https:\/\/doi.org\/10.1007\/s10898-015-0319-y","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,12]]}}}