期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 74, 期 16, 页码 5286-5302出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2011.05.005
关键词
Iterative schemes; Variational inequality; Fixed point; Constrained convex minimization; Nonexpansive mapping
资金
- National Science Foundation of China [11071169]
- Shanghai Municipal Education Commission [09ZZ133]
- Shanghai Normal University [DZL707]
- Science and Technology Commission of Shanghai Municipality [075105118]
- Shanghai Leading Academic Discipline Project [S30405]
- [NSC 99-2115-M-110-004-MY3]
The present paper is divided into two parts. In the first part, we introduce implicit and explicit iterative schemes for finding the fixed point of a nonexpansive mapping defined on the closed convex subset of a real Hilbert space. We establish results on the strong convergence of the sequences generated by the proposed schemes to a fixed point of a nonexpansive mapping. Such a fixed point is also a solution of a variational inequality defined on the set of fixed points. In the second part, we propose implicit and explicit iterative schemes for finding the approximate minimizer of a constrained convex minimization problem and prove that the sequences generated by our schemes converge strongly to a solution of the constrained convex minimization problem. Such a solution is also a solution of a variational inequality defined over the set of fixed points of a nonexpansive mapping. The results of this paper extend and improve several results presented in the literature in the recent past. (C) 2011 Elsevier Ltd. All rights reserved.
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