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Received October 4, 2018; Accepted December 21, 2019; Published December 31, 2018
Abstract. Let be a real Hilbert space. In this paper, we propose a new self-adaptive hybrid steepest descent algorithm for solving a variational inequality problem VI, were is a boundedly Lipschitz continuous (i.e., Lipschitz continuous on any bounded subset of ) and strongly monotone operator and is a nonexpansive mapping with a nonempty fixed point set . The strong convergence of our proposed algorithm is proved and the convergence rate estimation is also obtained. The advantage of our algorithm is that it does not require a priori knowledge of the Lipschitz constant of on any bounded subset of and also the strong monotone coefficient.
How to Cite this Article:
Songnian He, Lili Liu, Xiaolong Qin, A self-adaptive hybrid steepest descent algorithm for solving a class of variational inequalities, Journal of Nonlinear Functional Analysis, Vol. 2018 (2018), Article ID 49, pp. 1-9.