Generalized mixed equilibria, variational inequalities and constrained convex minimization
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Authors
Lu-Chuan Ceng
- Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China.
Ching-Feng Wen
- Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan.
- Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 807, Taiwan.
Abstract
In this paper, we introduce one multistep relaxed implicit extragradient-like scheme and another multistep relaxed explicit
extragradient-like scheme for finding a common element of the set of solutions of the minimization problem for a convex and
continuously Fréchet differentiable functional, the set of solutions of a finite family of generalized mixed equilibrium problems
and the set of solutions of a finite family of variational inequalities for inverse strongly monotone mappings in a real Hilbert
space. Under suitable control conditions, we establish the strong convergence of these two multistep relaxed extragradient-like
schemes to the same common element of the above three sets, which is also the unique solution of a variational inequality
defined over the intersection of the above three sets.
Share and Cite
ISRP Style
Lu-Chuan Ceng, Ching-Feng Wen, Generalized mixed equilibria, variational inequalities and constrained convex minimization, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 789--804
AMA Style
Ceng Lu-Chuan, Wen Ching-Feng, Generalized mixed equilibria, variational inequalities and constrained convex minimization. J. Nonlinear Sci. Appl. (2017); 10(2):789--804
Chicago/Turabian Style
Ceng, Lu-Chuan, Wen, Ching-Feng. "Generalized mixed equilibria, variational inequalities and constrained convex minimization." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 789--804
Keywords
- Convex minimization problem
- generalized mixed equilibrium problem
- variational inequality
- inverse-strongly monotone mapping.
MSC
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