{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T10:47:43Z","timestamp":1775040463818,"version":"3.50.1"},"reference-count":28,"publisher":"Pleiades Publishing Ltd","issue":"10","license":[{"start":{"date-parts":[[2015,10,1]],"date-time":"2015-10-01T00:00:00Z","timestamp":1443657600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,10,1]],"date-time":"2015-10-01T00:00:00Z","timestamp":1443657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput. Math. and Math. Phys."],"published-print":{"date-parts":[[2015,10]]},"DOI":"10.1134\/s0965542515100127","type":"journal-article","created":{"date-parts":[[2015,10,18]],"date-time":"2015-10-18T19:56:22Z","timestamp":1445198182000},"page":"1633-1641","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The dines theorem and some other properties of quadratic mappings"],"prefix":"10.1134","volume":"55","author":[{"given":"D. Yu.","family":"Karamzin","sequence":"first","affiliation":[]}],"member":"137","published-online":{"date-parts":[[2015,10,17]]},"reference":[{"key":"82_CR1","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1090\/S0002-9904-1941-07494-X","volume":"47","author":"L. L. Dines","year":"1941","unstructured":"L. L. Dines, \u201cOn the mapping of quadratic forms,\u201d Bull. Am. Math. Soc. 47, 494\u2013498 (1941).","journal-title":"Bull. Am. Math. Soc."},{"key":"82_CR2","first-page":"34","volume":"1","author":"A. V. Arutyunov","year":"2000","unstructured":"A. V. Arutyunov and V. K. Ja imovi, \u201cOn the theory of abnormal extremal problems,\u201d Vestn. Mosk. Gos. Univ., Ser. Vychisl. Mat. Kibern., No. 1, 34\u201340 (2000).","journal-title":"Vestn. Mosk. Gos. Univ., Ser. Vychisl. Mat. Kibern."},{"key":"82_CR3","volume-title":"Optimization Methods","author":"F. P. Vasil\u2019ev","year":"2002","unstructured":"F. P. Vasil\u2019ev, Optimization Methods (Faktorial, Moscow, 2002) [in Russian]."},{"key":"82_CR4","volume-title":"Introduction to Optimization","author":"B. T. Polyak","year":"1987","unstructured":"B. T. Polyak, Introduction to Optimization (Nauka, Moscow, 1983; Optimization Software, New York, 1987)."},{"issue":"9","key":"82_CR5","first-page":"1259","volume":"41","author":"B. T. Polyak","year":"2001","unstructured":"B. T. Polyak, \u201cLocal programming,\u201d Comput. Math. Math. Phys.41(9), 1259\u20131266 (2001).","journal-title":"Comput. Math. Math. Phys."},{"issue":"3","key":"82_CR6","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1023\/A:1021798932766","volume":"99","author":"B. T. Polyak","year":"1998","unstructured":"B. T. Polyak, \u201cConvexity of quadratic transformations and its use in control and optimization,\u201d J. Optim. Theor. Appl.99(3), 553\u2013583 (1998).","journal-title":"J. Optim. Theor. Appl."},{"issue":"5","key":"82_CR7","doi-asserted-by":"publisher","first-page":"2531","DOI":"10.1007\/BF02673841","volume":"100","author":"A. S. Matveev","year":"2000","unstructured":"A. S. Matveev and V. A. Yakubovich, \u201cNonconvex global optimization problems in control theory,\u201d J. Math. Sci.100(5), 2531\u20132563 (2000).","journal-title":"J. Math. Sci."},{"issue":"2","key":"82_CR8","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/s00245-001-0034-6","volume":"45","author":"J.-B. Hiriart-Urruty","year":"2002","unstructured":"J.-B. Hiriart-Urruty and M. Torki, \u201cPermanently going back and forth between the \u2018quadratic world\u2019 and the \u2018convexity world\u2019 in optimization,\u201d J. Appl. Math. Optim.45(2), 169\u2013184 (2002).","journal-title":"J. Appl. Math. Optim."},{"key":"82_CR9","doi-asserted-by":"crossref","unstructured":"P. Finsler, \u201cUber das Vorkommen definiter und semidefiniter Formen in Scharen quadratischer Formen,\u201d Comment. Math. Helv. 9, 188\u2013192 (1936\/1937).","DOI":"10.1007\/BF01258188"},{"key":"82_CR10","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1090\/S0002-9939-1961-0122827-1","volume":"12","author":"L. Brickman","year":"1961","unstructured":"L. Brickman, \u201cOn the fields of values of a matrix,\u201d Proc. Am. Math. Soc. 12, 61\u201366 (1961).","journal-title":"Proc. Am. Math. Soc."},{"issue":"3","key":"82_CR11","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/0041-5553(85)90069-2","volume":"25","author":"E. R. Avakov","year":"1985","unstructured":"E. R. Avakov, \u201cExtremum conditions for smooth problems with equality-type constraints,\u201d USSR Comput. Math. Math. Phys.25(3), 24\u201332 (1985).","journal-title":"USSR Comput. Math. Math. Phys."},{"issue":"4","key":"82_CR12","doi-asserted-by":"publisher","first-page":"1892","DOI":"10.1007\/BF01095139","volume":"55","author":"A. A. Agrachev","year":"1991","unstructured":"A. A. Agrachev and R. V. Gamkrelidze, \u201cQuadratic maps and smooth vector-valued functions: Euler characteristics of level sets,\u201d J. Sov. Math.55(4), 1892\u20131928 (1991).","journal-title":"J. Sov. Math."},{"issue":"5","key":"82_CR13","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/BF01158081","volume":"47","author":"E. R. Avakov","year":"1990","unstructured":"E. R. Avakov, \u201cTheorems on estimates in the neighborhood of a singular point of a mapping,\u201d Math. Notes47(5), 425\u2013432 (1990).","journal-title":"Math. Notes"},{"issue":"6","key":"82_CR14","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/s0294-1449(16)30118-4","volume":"13","author":"A. A. Agrachev","year":"1996","unstructured":"A. A. Agrachev and A. V. Sarychev, \u201cAbnormal sub-Riemannian geodesies: Morse index and rigidity,\u201d Ann. Inst. Henri Poincare13(6), 635\u2013690 (1996).","journal-title":"Ann. Inst. Henri Poincare"},{"key":"82_CR15","first-page":"787","volume":"7","author":"A. Matveev","year":"1996","unstructured":"A. Matveev, \u201cLagrange duality in nonconvex optimization theory and modifications of the Toeplitz\u2013Hausdorff theorem,\u201d St. Petersburg Math. J. 7, 787\u2013815 (1996).","journal-title":"St. Petersburg Math. J."},{"key":"82_CR16","first-page":"30","volume":"2","author":"A. V. Arutyunov","year":"1999","unstructured":"A. V. Arutyunov, \u201cSome properties of quadratic maps,\u201d Vestn. Mosk. Gos. Univ., Ser. 15: Vychisl. Mat, Kibern., No. 2, 30\u201332 (1999).","journal-title":"Vestn. Mosk. Gos. Univ., Ser. 15: Vychisl. Mat, Kibern."},{"key":"82_CR17","volume-title":"Preprint","author":"A. I. Barvinok","year":"1999","unstructured":"A. I. Barvinok, \u201cOn convex properties of the quadratic image of the sphere,\u201d Preprint (University of Michigan, 1999)."},{"issue":"1","key":"82_CR18","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1137\/S1052623403427264","volume":"15","author":"A. F. Izmailov","year":"2004","unstructured":"A. F. Izmailov and M. V. Solodov, \u201cNewton-type methods for optimization problems without constraint qualifications,\u201d SIAM J. Optim.15(1), 210\u2013228 (2004).","journal-title":"SIAM J. Optim."},{"issue":"8","key":"82_CR19","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1134\/S0965542506080045","volume":"46","author":"M. M. Golishnikov","year":"2006","unstructured":"M. M. Golishnikov and A. F. Izmailov, \u201cNewton-type methods for constrained optimization with nonregular constraints,\u201d Comput. Math. Math. Phys.46(8), 1299\u20131319 (2006).","journal-title":"Comput. Math. Math. Phys."},{"key":"82_CR20","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1134\/S0081543810040036","volume":"271","author":"A. V. Arutyunov","year":"2010","unstructured":"A. V. Arutyunov and S. E. Zhukovskiy, \u201cExistence and properties of inverse mappings,\u201d Proc. Steklov Inst. Math. 271, 12\u201322 (2010).","journal-title":"Proc. Steklov Inst. Math."},{"issue":"3","key":"82_CR21","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s10688-012-0028-y","volume":"46","author":"A. V. Arutyunov","year":"2012","unstructured":"A. V. Arutyunov, \u201cTwo problems of the theory of quadratic maps,\u201d Funct. Anal. Appl.46(3), 225\u2013227 (2012).","journal-title":"Funct. Anal. Appl."},{"issue":"3","key":"82_CR22","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1070\/RM2012v067n03ABEH004793","volume":"67","author":"A. V. Arutyunov","year":"2012","unstructured":"A. V. Arutyunov, \u201cSmooth abnormal problems in extremum theory and analysis,\u201d Russ. Math. Surv.67(3), 402\u2013457 (2012).","journal-title":"Russ. Math. Surv."},{"issue":"10","key":"82_CR23","doi-asserted-by":"publisher","first-page":"1342","DOI":"10.1134\/S0965542512100065","volume":"52","author":"A. V. Arutyunov","year":"2012","unstructured":"A. V. Arutyunov, S. E. Zhukovskiy, and Z. T. Mingaleeva, \u201cDifferential properties of the minimum function for diagonalizable quadratic problems,\u201d Comput. Math. Math. Phys.52(10), 1342\u20131350 (2012).","journal-title":"Comput. Math. Math. Phys."},{"issue":"1","key":"82_CR24","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s10107-010-0413-3","volume":"122","author":"A. F. Izmailov","year":"2012","unstructured":"A. F. Izmailov and M. V. Solodov, \u201cStabilized SQP revisited,\u201d Math. Program.122(1), 93\u2013120 (2012).","journal-title":"Math. Program."},{"key":"82_CR25","volume-title":"Real Algebraic Geometry","author":"J. Bochnak","year":"1988","unstructured":"J. Bochnak, M. Coste, and M. F. Roy, Real Algebraic Geometry (Springer, New York, 1988)."},{"issue":"6","key":"82_CR26","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1070\/SM2011v202n06ABEH004166","volume":"202","author":"A. V. Arutyunov","year":"2011","unstructured":"A. V. Arutyunov and D. Yu. Karamzin, \u201cRegular zeros of quadratic maps and their application,\u201d Sb. Math.202(6), 783\u2013806 (2011).","journal-title":"Sb. Math."},{"issue":"2","key":"82_CR27","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1134\/S0001434608070171","volume":"84","author":"A. V. Arutyunov","year":"2008","unstructured":"A. V. Arutyunov, \u201cNonnegativity of quadratic forms on intersections of quadrics and quadratic maps,\u201d Math. Notes84(2), 155\u2013165 (2008).","journal-title":"Math. Notes"},{"issue":"2","key":"82_CR28","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1070\/IM2014v078n02ABEH002686","volume":"78","author":"E. R. Avakov","year":"2014","unstructured":"E. R. Avakov, A. V. Arutyunov, and D. Yu. Karamzin, \u201cAn investigation of smooth maps in a neighborhood of an abnormal point,\u201d Izv. Math.78(2), 213\u2013250 (2014).","journal-title":"Izv. Math."}],"container-title":["Computational Mathematics and Mathematical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0965542515100127.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0965542515100127","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1134\/S0965542515100127","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0965542515100127.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T06:27:47Z","timestamp":1773728867000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0965542515100127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10]]},"references-count":28,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2015,10]]}},"alternative-id":["82"],"URL":"https:\/\/doi.org\/10.1134\/s0965542515100127","relation":{},"ISSN":["0965-5425","1555-6662"],"issn-type":[{"value":"0965-5425","type":"print"},{"value":"1555-6662","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10]]},"assertion":[{"value":"13 January 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 October 2015","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}