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Iterative Algorithms for Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-01
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
Consider the variational inequality VI(C,F) of finding a point x*∈C satisfying the property 〈Fx*,x-x*〉≥0 for all x∈C, where C is a level set of a convex function defined on a real Hilbert space H and F:H→H is a boundedly Lipschitzian (i.e., Lipschitzian on bounded subsets of H) and strongly monotone operator.
He and Xu proved that this variational inequality has a unique solution and devised iterative algorithms to approximate this solution (see He and Xu, 2009).
In this paper, relaxed and self-adaptive iterative algorithms are proposed for computing this unique solution.
Since our algorithms avoid calculating the projection PC (calculating PC by computing a sequence of projections onto half-spaces containing the original domain C) directly and select the stepsizes through a self-adaptive way (having no need to know any information of bounded Lipschitz constants of F (i.e., Lipschitz constants on some bounded subsets of H)), the implementations of our algorithms are very easy.
The algorithms in this paper improve and extend the corresponding results of He and Xu.
American Psychological Association (APA)
Yang, Caiping& He, Songnian. 2015. Iterative Algorithms for Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators. Journal of Applied Mathematics،Vol. 2015, no. 2015, pp.1-7.
https://search.emarefa.net/detail/BIM-1067044
Modern Language Association (MLA)
Yang, Caiping& He, Songnian. Iterative Algorithms for Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators. Journal of Applied Mathematics No. 2015 (2015), pp.1-7.
https://search.emarefa.net/detail/BIM-1067044
American Medical Association (AMA)
Yang, Caiping& He, Songnian. Iterative Algorithms for Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators. Journal of Applied Mathematics. 2015. Vol. 2015, no. 2015, pp.1-7.
https://search.emarefa.net/detail/BIM-1067044
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1067044