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Relaxed extragradient iterative methods for variational inequalities. (English) Zbl 1229.65109
Summary: We suggest and analyze some new relaxed extragradient iterative methods for finding a common element of the solution set of a variational inequality, the solution set of a general system of variational inequalities and the set of fixed points of a strictly pseudo-contractive mapping defined on a real Hilbert space. Strong convergence of the proposed methods under some mild conditions is established.
MSC:
65K15Numerical methods for variational inequalities and related problems
49J40Variational methods including variational inequalities
49M25Discrete approximations in calculus of variations
References:
[1]Bnouhachem, A.; Noor, M. A.; Hao, Z.: Some new extragradient iterative methods for variational inequalities, Nonlinear anal. 70, 1321-1329 (2009) · Zbl 1171.47050 · doi:10.1016/j.na.2008.02.014
[2]Ceng, L. C.; Ansari, Q. H.; Yao, J. C.: Viscosity approximation methods for generalized equilibrium problems and fixed point problems, J. global optim. 43, 487-502 (2009) · Zbl 1172.47045 · doi:10.1007/s10898-008-9342-6
[3]Ceng, L. C.; Huang, S.: Modified extragradient methods for strict pseudo-contractions and monotone mappings, Taiwanese J. Math. 13, No. 4, 1197-1211 (2009) · Zbl 1184.47034
[4]Ceng, L. C.; Wang, C. Y.; Yao, J. C.: Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. methods oper. Res. 67, 375-390 (2008) · Zbl 1147.49007 · doi:10.1007/s00186-007-0207-4
[5]Ceng, L. C.; Yao, J. C.: An extragradient-like approximation method for variational inequality problems and fixed point problems, Appl. math. Comput. 190, 205-215 (2007) · Zbl 1124.65056 · doi:10.1016/j.amc.2007.01.021
[6]Ceng, L. C.; Yao, J. C.: Relaxed viscosity approximation methods for fixed point problems and variational inequality problems, Nonlinear anal. 69, 3299-3309 (2008) · Zbl 1163.47052 · doi:10.1016/j.na.2007.09.019
[7]Iiduka, H.; Takahashi, W.: Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear anal. 61, 341-350 (2005) · Zbl 1093.47058 · doi:10.1016/j.na.2003.07.023
[8]Korpelevich, G. M.: An extragradient method for finding saddle points and for other problems, Ekon. mate. Metody 12, 747-756 (1976)
[9]Lions, J. L.; Stampacchia, G.: Variational inequalities, Commun. pure appl. Math. 20, 493-512 (1967) · Zbl 0152.34601 · doi:10.1002/cpa.3160200302
[10]Marino, G.; Xu, H. K.: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. math. Anal. appl. 329, 336-346 (2007) · Zbl 1116.47053 · doi:10.1016/j.jmaa.2006.06.055
[11]Nadezhkina, N.; Takahashi, W.: Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings, J. optim. Theory appl. 128, 191-201 (2006) · Zbl 1130.90055 · doi:10.1007/s10957-005-7564-z
[12]Nadezhkina, N.; Takahashi, W.: Strong convergence theorem by a hybrid method for nonexpansive mappings and Lipschitz-continuous monotone mappings, SIAM J. Optim. 16, No. 4, 1230-1241 (2006) · Zbl 1143.47047 · doi:10.1137/050624315
[13]Suzuki, T.: Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals, J. math. Anal. appl. 305, 227-239 (2005) · Zbl 1068.47085 · doi:10.1016/j.jmaa.2004.11.017
[14]Takahashi, W.; Toyoda, M.: Weak convergence theorems for nonexpansive mappings and monotone mappings, J. optim. Theory appl. 118, 417-428 (2003) · Zbl 1055.47052 · doi:10.1023/A:1025407607560
[15]Verma, R. U.: On a new system of nonlinear variational inequalities and associated iterative algorithms, Math. sci. Res. hot-line 3, No. 8, 65-68 (1999) · Zbl 0970.49011
[16]Xu, H. K.; Kim, T. H.: Convergence of hybrid steepest-descent methods for variational inequalities, J. optim. Theory appl. 119, No. 1, 185-201 (2003) · Zbl 1045.49018 · doi:10.1023/B:JOTA.0000005048.79379.b6
[17]Yao, Y.; Liou, Y. C.; Kang, S. M.: Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method, Comput. math. Appl. 59, 3472-3480 (2010) · Zbl 1197.49008 · doi:10.1016/j.camwa.2010.03.036
[18]Zeng, L. C.; Wong, N. C.; Yao, J. C.: Strong convergence theorems for strictly pseudocontractive mappings of Browder – petryshyn type, Taiwanese J. Math. 10, 837-849 (2006) · Zbl 1159.47054
[19]Zeng, L. C.; Yao, J. C.: Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems, Taiwanese J. Math. 10, 1293-1303 (2006) · Zbl 1110.49013