Title | A new variant of regularization for extragradient methods |
Publication Type | Journal Article |
Year of Publication | 2014 |
Authors | Semenov, VV, Chabak, LM |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2014.10.045 |
Issue | 10 |
Section | Information Science and Cybernetics |
Pagination | 45-50 |
Date Published | 10/2014 |
Language | Ukrainian |
Abstract | The article suggests a new regularization scheme of extragradient type methods to solve monotone variational inequalities in an infinite-dimensional Hilbert space. The theorem on strong convergence to the normal solution of the variational inequality for a regularized basic variant of the extragradient method is proved. |
Keywords | extragradient methods, regularization |
1. Kinderlerer D., Stampakkia G. Introduction to variational inequalities and their applications, Moscow: Mir, 1983 (in Russian).
2. Facchinei F., Pang J.-S. Finite-dimensional variational inequalities and complementarity problem. Vol. 2., New York: Springer, 2003.
3. Takahashi W., Takeuchi Y., Kubota R. J. Math. Anal. Appl., 2008, 341: 276–286. https://doi.org/10.1016/j.jmaa.2007.09.062
4. Semenov V. V. Zhurn. obchysl. ta prykl. matamatyky 2013, No 1(111):. 46–56 (in Ukrainian).
5. Korpelevich G. M. Ekonomika i mat. metody, 1976, 12, No 4: 747–756 (in Russian).
6. Tseng P. SIAM J. Control Optim., 2000, 38: 431–446. https://doi.org/10.1137/S0363012998338806
7. Censor Y., Gibali A., Reich S. J. of Optitmization Theory and Applications, 2011, 148: 318–335.
8. Lyashko S. I., Semenov V. V., Voitova T. A. Kibernetika i sistemnyi analiz, 2011, No 4: 146–154 (in Russian).
9. Voitova T. A., Denysov S. V., Semenov V. V. Zhurn. obchysl. ta prykl. matematyky, 2011, No 1(104): 10–23 (in Ukrainian).
10. Apostol R. Ya., Grynenko A. A., Semenov V. V Zhurn. obchysl. ta prykl. matematyky, 2012, No 1(107): 3–14 (in Ukrainian) (in Ukrainian).
11. Malitsky Yu. V., Semenov V. V. J. of Global Optimization, 2014. doi:10.1007/s10898-014-0150-x. https://doi.org/10.1007/s10898-014-0150-x
12. Malitsky Yu. V., Semenov V. V. Kibernetika i sistemnyi analiz, 2014, No 2: 125–131 (in Russian).
13. Nadezhkina N., Takahashi W. SIAM J. Optim., 2006, 16: 1230–1241. https://doi.org/10.1137/050624315
14. Censor Y., Gibali A., Reich S. Optimization Methods and Software, 2011, 26: 827–845. https://doi.org/10.1080/10556788.2010.551536