Geodesic
Reduction of variational inequalities with irregular operators on a~ball to regular operator equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2013), pp. 32-41.

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We propose a method for reducing variational inequalities defined by general smooth irregular operators on a ball in a Hilbert space to equivalent regular operator equations. The mentioned equations involve the operator of metric projection on the boundary of the ball. We establish conditions which guarantee the local strong monotonicity of the obtained equations. We discuss applications to the problem of finding normed eigenvectors of nonlinear operators.
Keywords: variational inequality, smooth operator, irregular operator, operator equation, eigenvector. 
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M. Yu. Kokurin. Reduction of variational inequalities with irregular operators on a~ball to regular operator equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2013), pp. 32-41. http://geodesic.mathdoc.fr/item/IVM_2013_4_a3/

[1] Bakushinskii A. B., Kokurin M. Yu., Yusupova N. A., “Neobkhodimye usloviya skhodimosti iteratsionnykh metodov resheniya nelineinykh operatornykh uravnenii bez svoistva regulyarnosti”, Zhurn. vychisl. matem. i matem. fiz., 40:7 (2000), 986–996 | MR | Zbl

[2] Kokurin M. Yu., “Ob organizatsii globalnogo poiska pri realizatsii skhemy Tikhonova”, Izv. vuzov. Matem., 2010, no. 12, 20–31 | MR | Zbl

[3] Kokurin M. Yu., “On sequential minimization of Tikhonov functionals in ill-posed problems with a priori information on solutions”, J. Inverse and Ill-posed Problems, 18:9 (2011), 1031–1050 | MR

[4] Bakushinskii A. B., Kokurin M. Yu., Iteratsionnye metody resheniya nekorrektnykh operatornykh uravnenii s gladkimi operatorami, Editorial URSS, M., 2002

[5] Vasilev F. P., Ishmukhametov A. Z., Potapov M. M., Obobschennyi metod momentov v zadachakh optimalnogo upravleniya, Izd-vo MGU, M., 1989 | MR

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

[7] Bakushinskii A. B., Goncharskii A. V., Iterativnye metody resheniya nekorrektnykh zadach, Nauka, M., 1989 | MR

[8] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 1980 | MR | Zbl

[9] Izmailov A. F., Tretyakov A. A., 2-regulyarnye metody resheniya nelineinykh zadach. Teoriya i chislennye metody, Fizmatlit, M., 1999 | MR

[10] Arnold V. I., Obyknovennye differentsialnye uravneniya, Nauka, M., 1975 | MR | Zbl

[11] Bakushinskii A. B., Kokurin M. Yu., Iteratsionnye metody resheniya neregulyarnykh uravnenii, LENAND, M., 2006

[12] Krasnoselskii M. A., Vainikko G. M., Zabreiko P. P., Rutitskii Ya. B., Stetsenko V. Ya., Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969 | MR

[13] Polyak B. T., “Lokalnoe programmirovanie”, Zhurn. vychisl. matem. i matem. fiz., 41:9 (2001), 1324–1331 | MR | Zbl

[14] Krasnoselskii M. A., Zabreiko P. P., Geometricheskie metody nelineinogo analiza, Nauka, M., 1975 | MR

[15] Dymarskii Ya. M., “Metod mnogoobrazii v teorii sobstvennykh vektorov nelineinykh operatorov”, Sovremennaya matematika. Fundamentalnye napravleniya, 24, 2007, 3–159 | MR | Zbl

[16] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR