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The subgradient extragradient method for solving variational inequalities in Hilbert space. (English) Zbl 1229.58018
Authors’ abstract: We present a subgradient extragradient method for solving variational inequalities in Hilbert space. In addition, we propose a modified version of our algorithm that finds a solution of a variational inequality which is also a fixed point of a given nonexpansive mapping. We establish weak convergence theorems for both algorithms.
MSC:
58E35Variational inequalities (global problems)
References:
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[10]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
[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]Browder, F.E.: Fixed point theorems for noncompact mappings in Hilbert space. Proc. Natl. Acad. Sci. USA 53, 1272–1276 (1965) · Zbl 0125.35801 · doi:10.1073/pnas.53.6.1272