Multi-step hybrid steepest-descent methods for split feasibility problems with hierarchical variational inequality problem constraints
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Authors
L. C. Ceng
- Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China.
Y. C. Liou
- Department of Healthcare Administration and Medical Informatics, Kaohsiung Medical University, Kaohsiung 80708, Taiwan.
D. R. Sahu
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India.
Abstract
In this paper, we introduce and analyze a multi-step hybrid steepest-descent algorithm by combining Korpelevich's
extragradient method, viscosity approximation method, hybrid steepest-descent method, Mann's
iteration method and gradient-projection method (GPM) with regularization in the setting of infinite-dimensional
Hilbert spaces. Strong convergence was established.
Share and Cite
ISRP Style
L. C. Ceng, Y. C. Liou, D. R. Sahu, Multi-step hybrid steepest-descent methods for split feasibility problems with hierarchical variational inequality problem constraints, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4148--4166
AMA Style
Ceng L. C., Liou Y. C., Sahu D. R., Multi-step hybrid steepest-descent methods for split feasibility problems with hierarchical variational inequality problem constraints. J. Nonlinear Sci. Appl. (2016); 9(6):4148--4166
Chicago/Turabian Style
Ceng, L. C., Liou, Y. C., Sahu, D. R.. "Multi-step hybrid steepest-descent methods for split feasibility problems with hierarchical variational inequality problem constraints." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4148--4166
Keywords
- Hybrid steepest-descent method
- split feasibility problem
- generalized mixed equilibrium problem
- variational inclusion
- maximal monotone mapping
- nonexpansive mapping.
MSC
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