Far Eastern Mathematical Journal

To content of the issue


The methods for solution semicoercive variational inequalities of mechanics on the basis of modified Lagrangian functionals


Vikhtenko E. M., Woo G., Namm R. V.

2014, issue 1, Ń. 6-17


Abstract
The duality scheme based on a modified Lagrangian functional is considered for an elliptic semi-coercive variational Signorini’s inequality. The sustainable method for the solution of an investigated inequality is constructed and justified.

Keywords:
variational inequality, Signorini’s problem, sensitivity functional, Lagrangian functional, dual functional, saddle point, Uzawa method, proximal regularization

Download the article (PDF-file)

References

[1] G. Fikera, Teoremy sushchestvovaniia v teorii uprugosti, Mir, M., 1974.
[2] R. Glovinski, Zh.L. Lions, R. Tremol'er, Chislennoe issledovanie variatsionnykh neravenstv, Mir, M, 1979.
[3] 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.
[4] I. Glavachek, Ia. Gaslinger, I. Nechas, Ia. Lovishek, Reshenie variatsionnykh neravenstv v mekhanike, Mir, M., 1986.
[5] G. Diuvo, Zh.-L. Lions, Neravenstva v mekhanike i fizike, Nauka, M., 1980.
[6] A. M. Khludnev, Zadachi teorii uprugosti v negladkikh oblastiakh, Fizmatlit, M., 2010.
[7] W. Mclean, Strongly Elliptic Systems and Boundary Integral Equations, University Press, Cambridge, United Kingdom, 2000.
[8] I. Ekland, R. Temam, Vypuklyi analiz i variatsionnye problemy, Mir, M., 1979.
[9] D.P. Bertsecas, Convex Optimization Theory, Athena Scientific, Massachusetts Institute of Technology, Massachusetts, USA, 2009.
[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] E. M. Vikhtenko, R. V. Namm, “Kharakteristicheskie svoistva modifitsirovannogo funktsionala Lagranzha dlia kontaktnoi zadachi teorii uprugosti s zadannym treniem”, Dal'nevost. matem. zhurn., 9:1–2 (2009), 38–47.
[12] A. Kufner, S. Fuchik, Nelineinye differentsial'nye uravneniia, Nauka, M., 1988.
[13] N. N. Kushniruk, R. V. Namm, “Metod mnozhitelei Lagranzha dlia resheniia polukoertsitivnoi model'noi zadachi s treniem”, Sibirskii zh. vychisl. matem., 12:4 (2009), 409–420.
[14] L. V. Kantorovich, G. L. Akilov, Funktsional'nyi analiz, Nauka, M, 1984.
[15] B.T. Poliak, Vvedenie v optimizatsiiu, Nauka, M, 1983.
[16] R. V. Namm, A. G. Podgaev, “O W_2^2 -reguliarnosti reshenii polukoertsitivnykh variatsionnykh neravenstv”, Dal'nevostochnyi matem. zhurn., 3:2 (2002), 210–215.

To content of the issue