Convergence of an extragradient-type method for variational inequality with applications to optimal control problems

Our aim in this paper is to introduce an extragradient-type method for solving variational inequality with uniformly continuous pseudomonotone operator. The strong convergence of the iterative sequence generated by our method is established in real Hilbert spaces. Our method uses computationally ine...

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Bibliographic Details
Published in:Numerical algorithms Vol. 81; no. 1; pp. 269 - 291
Main Authors: Vuong, Phan Tu, Shehu, Yekini
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2019
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computational mathematics
Computer Science
Convergence
Differential equations
Hilbert space
Iterative methods
Mathematical analysis
Numeric Computing
Numerical Analysis
Operators (mathematics)
Optimal control
Ordinary differential equations
Original Paper
Theory of Computation
Hilbert spaces
Strong convergence
Pseudomonotone operator
Variational inequality
Optimal control problem
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:Our aim in this paper is to introduce an extragradient-type method for solving variational inequality with uniformly continuous pseudomonotone operator. The strong convergence of the iterative sequence generated by our method is established in real Hilbert spaces. Our method uses computationally inexpensive Armijo-type linesearch procedure to compute the stepsize under reasonable assumptions. Finally, we give numerical implementations of our results for optimal control problems governed by ordinary differential equations.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-018-0547-6