Inertial projection and contraction algorithms for variational inequalities

In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space H . In addition, we propose a modified version of our algorithm to find a common...

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Bibliographic Details
Published inJournal of global optimization Vol. 70; no. 3; pp. 687 - 704
Main Authors Dong, Q. L., Cho, Y. J., Zhong, L. L., Rassias, Th. M.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2018
Springer
Springer Nature B.V
Subjects
Algorithms
Computer Science
Fixed points (mathematics)
Hilbert space
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Portfolio management
Projection
Real Functions
Signal processing
49J35
Projection and contraction algorithm
Extragradient algorithm
Inertial type algorithm
Variational inequality
90C47
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Summary:In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space H . In addition, we propose a modified version of our algorithm to find a common element of the set of solutions of a variational inequality and the set of fixed points of a nonexpansive mapping in H . We establish weak convergence theorems for both proposed algorithms. Finally, we give the numerical experiments to show the efficiency and advantage of the inertial projection and contraction algorithm.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-017-0506-0