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Weak convergence of a projection algorithm for variational inequalities in a Banach space |
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| Authors: | Hideaki Iiduka Wataru Takahashi |
| Affiliation: | a Department of Communications and Integrated Systems, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan b Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8522, Japan |
| Abstract: | Let C be a nonempty, closed convex subset of a Banach space E. In this paper, motivated by Alber [Ya.I. Alber, Metric and generalized projection operators in Banach spaces: Properties and applications, in: A.G. Kartsatos (Ed.), Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, in: Lecture Notes Pure Appl. Math., vol. 178, Dekker, New York, 1996, pp. 15-50], we introduce the following iterative scheme for finding a solution of the variational inequality problem for an inverse-strongly-monotone operator A in a Banach space: x1=x∈C and xn+1=ΠCJ−1(Jxn−λnAxn) |
| Keywords: | Generalized projection Inverse-strongly-monotone operator Variational inequality p-Uniformly convex Weak convergence |
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