Far Eastern Mathematical Journal

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On the method of searching a saddle point of modified Lagrangian functional for elasticity problem with friction


E. M. Vikhtenko

2012, issue 1, Ń. 3–11


Abstract
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).

Keywords:
contact problem, modified Lagrangian functional, saddle point, Uzawa method

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References

[1] I. Glavachek, Ia. Gaslinger, I. Nechas, Ia. Lovishek, Reshenie variatsionnykh neravenstv v mekhanike, Mir, M., 1986.
[2] N. Kikuchi, T. Oden, Contact problem in elasticity: a study of variational inequalities and finite element methods, SIAM, Philadelphia, 1988.
[3] G. Fikera, Teoremy sushchestvovaniia v teorii uprugosti, Mir, M., 1974.
[4] E. M. Vikhtenko, R. V. Namm, “Skhema dvoistvennosti dlia resheniia polukoertsitivnoi zadachi Sin'orini s treniem”, Zh. vychisl. matem. i matem. fiz., 47:12 (2007), 2023–2036.
[5] R. Glovinski, Zh. L. Lions, R. Tremol'er, Chislennoe issledovanie variatsionnykh neravenstv, Mir, M, 1979.
[6] R. Glowinski, Numerical methods for nonlinear variational problems, Springer, New York, 1984.
[7] G. Vu, R. V. Namm, S. A. Sachkov, “Iteratsionnyi metod poiska sedlovoi tochki dlia polukoertsitivnoi zadachi Sin'orini, osnovannyi na modifitsirovannom funktsionale Lagranzha”, Zh. vychisl. matem. i matem. fiz., 46:1 (2006), 26–36.
[8] E. M. Vikhtenko, R. V. Namm, “Iterativnaia proksimal'naia reguliarizatsiia modifitsirovannogo funktsionala Lagranzha dlia resheniia polukoertsitivnogo kvazivariatsionnogo neravenstva Sin'orini”, Zh. vychisl. matem. i matem. fiz., 48:9 (2008), 1571–1579.
[9] E. M. Vikhtenko, R. V. Namm, “Kharakteristicheskie svoistva modifitsirovannogo funktsionala Lagranzha dlia kontaktnoi zadachi teorii uprugosti s zadannym treniem”, Dal'nevostochnyi matem. zhurnal, 9:1–2 (2009), 38–47.
[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.
[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. Poliak, Vvedenie v optimizatsiiu, Nauka, M, 1983.
[13] K. Grossman, A. A. Kaplan, Nelineinoe programmirovanie na osnove bezuslovnoi minimizatsii, Nauka, Novosibirsk, 1981.
[14] L. V. Kantorovich, G. L. Akimov, Funktsional'nyi analiz, Nauka, M, 1984.

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