On the method of searching a saddle point of modified Lagrangian functional for elasticity problem with friction
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 3-11.

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The semicoercive elasticity problem with the friction is considered. The scheme of duality with modified Lagrangian functional is used. A method of searching a saddle point of modified Lagrangian functional is constructed and proved with various step of shift according to dual variable. The main results of the paper were reported on the section talk at the International conference «Toric Topology and Automorphic Functions» (September, 5–10th, 2011, Khabarovsk, Russia).
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E. M. Vikhtenko. On the method of searching a saddle point of modified Lagrangian functional for elasticity problem with friction. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a0/

[1] I. Glavachek, Ya. Gaslinger, I. Nechas, Ya. Lovishek, Reshenie variatsionnykh neravenstv v mekhanike, Mir, M., 1986 | MR

[2] N. Kikuchi, T. Oden, Contact problem in elasticity: a study of variational inequalities and finite element methods, SIAM, Philadelphia, 1988 | MR | Zbl

[3] G. Fikera, Teoremy suschestvovaniya v teorii uprugosti, Mir, M., 1974

[4] E. M. Vikhtenko, R. V. Namm, “Skhema dvoistvennosti dlya resheniya polukoertsitivnoi zadachi Sinorini s treniem”, Zh. vychisl. matem. i matem. fiz., 47:12 (2007), 2023–2036 | MR

[5] R. Glovinski, Zh. L. Lions, R. Tremoler, Chislennoe issledovanie variatsionnykh neravenstv, Mir, M, 1979 | MR

[6] R. Glowinski, Numerical methods for nonlinear variational problems, Springer, New York, 1984 | MR | Zbl

[7] G. Vu, R. V. Namm, S. A. Sachkov, “Iteratsionnyi metod poiska sedlovoi tochki dlya polukoertsitivnoi zadachi Sinorini, osnovannyi na modifitsirovannom funktsionale Lagranzha”, Zh. vychisl. matem. i matem. fiz., 46:1 (2006), 26–36 | MR | Zbl

[8] E. M. Vikhtenko, R. V. Namm, “Iterativnaya proksimalnaya regulyarizatsiya modifitsirovannogo funktsionala Lagranzha dlya resheniya polukoertsitivnogo kvazivariatsionnogo neravenstva Sinorini”, Zh. vychisl. matem. i matem. fiz., 48:9 (2008), 1571–1579. | MR

[9] E. M. Vikhtenko, R. V. Namm, “Kharakteristicheskie svoistva modifitsirovannogo funktsionala Lagranzha dlya kontaktnoi zadachi teorii uprugosti s zadannym treniem”, Dalnevostochnyi matem. zhurnal, 9:1–2 (2009), 38–47 | MR

[10] E. M. Vikhtenko, G. Vu, R. V. Namm, “O skhodimosti metoda Udzavy s modifitsirovannym funktsionalom Lagranzha v variatsionnykh neravenstvakh mekhaniki”, Zh. vychisl. matem. i matem. fiz., 50:8 (2010), 1357–1366 | MR | Zbl

[11] R. V. Namm, E. M. Vikhtenko, “Modified Lagrangian Functional for Solving the Signorini Problem with Friction”, Advances in Mechanics Research, v. 1, Nova Science Publishers, New-York, 2010, 435–446

[12] B. T. Polyak, Vvedenie v optimizatsiyu, Nauka, M, 1983 | MR

[13] K. Grossman, A. A. Kaplan, Nelineinoe programmirovanie na osnove bezuslovnoi minimizatsii, Nauka, Novosibirsk, 1981 | Zbl

[14] L. V. Kantorovich, G. L. Akimov, Funktsionalnyi analiz, Nauka, M, 1984 | MR | Zbl