Convergence theorems of subgradient extragradient algorithm for solving variational inequalities and a convex feasibility problem

Let C be a nonempty closed and convex subset of a uniformly smooth and 2-uniformly convex real Banach space E with dual space E ∗ . In this paper, a Krasnoselskii-type subgradient extragradient iterative algorithm is constructed and used to approximate a common element of solutions of variational in...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering 2018-06, Vol.2018 (1), p.1-14, Article 16
Main Authors: Chidume, C. E., Nnakwe, M. O.
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Banach spaces
Differential Geometry
Fixed points (mathematics)
Iterative algorithms
Iterative Methods and Optimization Algorithms: A Dedication to Dr. Hong-Kun Xu
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Relatively nonexpansive maps
Subgradient extragradient algorithm
Theorems
Topology
Variational inequality
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Summary:Let C be a nonempty closed and convex subset of a uniformly smooth and 2-uniformly convex real Banach space E with dual space E ∗ . In this paper, a Krasnoselskii-type subgradient extragradient iterative algorithm is constructed and used to approximate a common element of solutions of variational inequality problems and fixed points of a countable family of relatively nonexpansive maps. The theorems proved are improvement of the results of Censor et al. (J. Optim. Theory Appl. 148:318–335, 2011 ).
ISSN:1687-1812
1687-1812
2730-5422
DOI:10.1186/s13663-018-0641-4