{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T16:25:23Z","timestamp":1774628723686,"version":"3.50.1"},"reference-count":17,"publisher":"Pleiades Publishing Ltd","issue":"7","license":[{"start":{"date-parts":[[2007,7,1]],"date-time":"2007-07-01T00:00:00Z","timestamp":1183248000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2007,7,1]],"date-time":"2007-07-01T00:00:00Z","timestamp":1183248000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput. Math. and Math. Phys."],"published-print":{"date-parts":[[2007,7]]},"DOI":"10.1134\/s0965542507070020","type":"journal-article","created":{"date-parts":[[2007,8,1]],"date-time":"2007-08-01T06:14:54Z","timestamp":1185948894000},"page":"1073-1100","source":"Crossref","is-referenced-by-count":2,"title":["Necessary extremum conditions in the optimal control problem with state constraints"],"prefix":"10.1134","volume":"47","author":[{"given":"D. Yu.","family":"Karamzin","sequence":"first","affiliation":[]}],"member":"137","reference":[{"key":"7002_CR1","first-page":"194","volume":"169","author":"V. I. Blagodatskikh","year":"1985","unstructured":"V. I. Blagodatskikh and A. F. Filippov, \u201cDifferential Inclusions and Optimal Control,\u201d in Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 169, 194\u2013252 (1985).","journal-title":"Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR"},{"key":"7002_CR2","volume-title":"Extremum Conditions: Abnormal and Degenerate Problems","author":"A. V. Arutyunov","year":"1997","unstructured":"A. V. Arutyunov, Extremum Conditions: Abnormal and Degenerate Problems (Faktorial, Moscow, 1997) [in Russian]."},{"key":"7002_CR3","first-page":"475","volume":"125","author":"R. V. Gamkrelidze","year":"1959","unstructured":"R. V. Gamkrelidze, \u201cTime-optimal Processes under Bounded Phase Coordinates,\u201d Dokl. Akad. Nauk SSSR 125, 475\u2013478 (1959).","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"7002_CR4","volume-title":"The Mathematical Theory of Optimal Processes","author":"L. S. Pontryagin","year":"1983","unstructured":"L. S. Pontryagin, V. G. Boltyanskil, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1983; Gordon and Breach, New York, 1986)."},{"issue":"3","key":"7002_CR5","first-page":"395","volume":"5","author":"A. Ya. Dubovitskii","year":"1965","unstructured":"A. Ya. Dubovitskii and A. A. Milyutin, \u201cConstrained Optimization Problems,\u201d Zh. Vychisl. Mat. Mat. Fiz. 5(3), 395\u2013453 (1965).","journal-title":"Zh. Vychisl. Mat. Mat. Fiz."},{"key":"7002_CR6","unstructured":"A. V. Arutyunov and N. T. Tynyanskii, \u201cOn the Maximum Principle in a Problem with State Constraints,\u201d Izv. Akad. Nauk SSSR, Ser. Tekhn. Kibern., No. 4, 60\u201368 (1984)."},{"key":"7002_CR7","first-page":"147","volume-title":"Itogi Nauki Tekh., Ser.: Mat. Anal.","author":"A. V. Arutyunov","year":"1989","unstructured":"A. V. Arutyunov, \u201cPerturbation of Constrained Optimization and Necessary Optimality Conditions,\u201d in Itogi Nauki Tekh., Ser.: Mat. Anal. (VINITI, Moscow, 1989), Vol. 27, pp. 147\u2013235 [in Russian]."},{"key":"7002_CR8","first-page":"1033","volume":"280","author":"A. V. Arutyunov","year":"1985","unstructured":"A. V. Arutyunov, \u201cOn Necessary Optimality Conditions in a Problem with State Constraints,\u201d Dokl. Akad. Nauk SSSR 280, 1033\u20131037 (1985).","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"7002_CR9","volume-title":"Optimal Control of Discontinuous Systems","author":"L. T. Ashchepkov","year":"1987","unstructured":"L. T. Ashchepkov, Optimal Control of Discontinuous Systems (Nauka, Novosibirsk, 1987) [in Russian]."},{"key":"7002_CR10","first-page":"372","volume":"13","author":"I. B. Russak","year":"1975","unstructured":"I. B. Russak, \u201cSecond-Order Necessary Conditions for General Problems with State Inequality Constraints,\u201d J. Optimizat. Theory Appl. 13, 372\u2013388 (1975).","journal-title":"J. Optimizat. Theory Appl."},{"key":"7002_CR11","unstructured":"D. Yu. Karamzin, \u201cOn the Theory of Maximum Principle in Problems with State Constraints,\u201d Vestn. Mosk. Univ., Ser. 15, Vychisl. Mat. Kibern., No. 4, 23\u201331 (2002)."},{"key":"7002_CR12","doi-asserted-by":"crossref","first-page":"305","DOI":"10.4213\/mzm2839","volume":"61","author":"A. D. Ioffe","year":"1997","unstructured":"A. D. Ioffe and V. M. Tikhomirov, \u201cSome Remarks on Variational Principles,\u201d Mat. Zametki 61, 305\u2013311 (1997).","journal-title":"Mat. Zametki"},{"key":"7002_CR13","volume-title":"Elements of the Theory of Functions and Functional Analysis","author":"A. N. Kolmogorov","year":"1968","unstructured":"A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Nauka, Moscow, 1968; Graylock, Albany, N. Y., 1961)."},{"key":"7002_CR14","volume-title":"Optimal Control","author":"V. M. Alekseev","year":"1979","unstructured":"V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control (Nauka, Moscow, 1979) [in Russian]."},{"key":"7002_CR15","volume-title":"Functional Analysis","author":"W. Rudin","year":"1973","unstructured":"W. Rudin, Functional Analysis (McGraw-Hill, New York, 1973; Mir, Moscow, 1975)."},{"key":"7002_CR16","first-page":"76","volume-title":"Theory and Applications of Nonlinear Analysis","author":"D. Yu. Karamzin","year":"2005","unstructured":"D. Yu. Karamzin, \u201cMaximum Principle and Second-Order Necessary Conditions in Optimal Control Problems with State Constraints,\u201d in Theory and Applications of Nonlinear Analysis (Vychisl. Tsentr Ross. Akad. Nauk, Moscow, 2005), pp. 76\u2013112 [in Russian]."},{"key":"7002_CR17","doi-asserted-by":"crossref","unstructured":"D. Yu. Karamzin, \u201cPrinciple of Maximum in the Problem of Control under Limited Phase Coordinates,\u201d Avtom. Telemekh., No. 2, 26\u201338 (2007) [Autom. Remote Control. 68, 233\u2013244 (2007)].","DOI":"10.1134\/S000511790702004X"}],"updated-by":[{"DOI":"10.1134\/s0965542508020164","type":"erratum","label":"Erratum","source":"publisher","updated":{"date-parts":[[2011,2,5]],"date-time":"2011-02-05T00:00:00Z","timestamp":1296864000000}}],"container-title":["Computational Mathematics and Mathematical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0965542507070020.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0965542507070020","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1134\/S0965542507070020","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0965542507070020.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T06:19:45Z","timestamp":1773728385000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0965542507070020"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,7]]},"references-count":17,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2007,7]]}},"alternative-id":["7002"],"URL":"https:\/\/doi.org\/10.1134\/s0965542507070020","relation":{},"ISSN":["0965-5425","1555-6662"],"issn-type":[{"value":"0965-5425","type":"print"},{"value":"1555-6662","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,7]]}}}