Geodesic
Continuous first-order methods for monotone inclusions in a Hilbert space
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 8, pp. 1241-1248 Cet article a éte moissonné depuis la source Math-Net.Ru

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Equations in a Hilbert space that involve multivalued monotone mappings are examined. Solutions to such equations are understood in the inclusion sense. A continuous first-order method and its regularized version are constructed on the basis of the resolvent of the maximal monotone operator, and sufficient conditions for them to converge strongly are obtained. 
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I. P. Ryazantseva. Continuous first-order methods for monotone inclusions in a Hilbert space. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 8, pp. 1241-1248. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_8_a2/

[1] Ryazantseva I. P., Izbpannye glavy teopii opepatopov monotonnogo tipa, Izdatelstvo NGTU, Nizhnii Novgopod, 2008

[2] Antipin A. S., “Nepreryvnye i iterativnye protsessy s operatorami proektirovaniya i tipa proektirovaniya”, Voprosy kibernetiki. Vychisl. voprosy analiza bolshikh sistem, Nauchnyi sovet po kompleksnoi probleme “Kibernetika” AN SSSR, M., 1989, 5–43 | MR

[3] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981 | MR

[4] Ryazantseva I. P., “Nepreryvnyi metod regulyarizatsii pervogo poryadka dlya smeshannykh variatsionnykh neravenstv”, Setochnye metody dlya kraevykh zadach i prilozheniya, Materialy vosmoi Vserossiiskoi konf., posvyasch. 80-letiyu so dnya rozhdeniya A. D. Lyashko (Kazan, 2010), 373–379

[5] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1988 | MR

[6] Alber Ya., Ryazantseva I., Nonlinear ill-posed problems of monotone type, Springer, Dordrecht, 2006 | MR

[7] Ivanov V. K., Vasin V. V., Tanana V. P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978 | MR

[8] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR

[9] Lyashko A. D., Karchevskii M. M., “O reshenii nekotorykh nelineinykh zadach teorii filtratsii”, Izv. vyssh. uchebn. zavedenii. Matematika, 1975, no. 6, 73–81 | Zbl

[10] Badriev I. B., Zadvornov O. A., Saddek A. M., “Issledovanie skhodimosti iteratsionnykh metodov resheniya nekotorykh variatsionnykh neravenstv s psevdomonotonnymi operatorami”, Differents. ur-niya, 37:7 (2001), 1009–1016 | MR

[11] Badriev I. B., Zadvornov O. A., “Iteratsionnye metody resheniya variatsionnykh neravenstv vtorogo roda s obratno silno monotonnymi operatorami”, Izv. vyssh. uchebn. zavedenii. Matematika, 2003, no. 1, 20–28 | MR | Zbl