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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Vydáno v:	Numerical algorithms Ročník 81; číslo 1; s. 269 - 291
Hlavní autoři:	Vuong, Phan Tu, Shehu, Yekini
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.05.2019 Springer Nature B.V
Témata:	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
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Abstract	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.
AbstractList	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.
Author	Vuong, Phan Tu Shehu, Yekini
Author_xml	– sequence: 1 givenname: Phan Tu surname: Vuong fullname: Vuong, Phan Tu email: phantuvuong@tdt.edu.vn organization: Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Faculty of Mathematics and Statistics, Ton Duc Thang University – sequence: 2 givenname: Yekini orcidid: 0000-0001-9224-7139 surname: Shehu fullname: Shehu, Yekini organization: Department of Mathematics, University of Nigeria, Institute of Mathematics, Campus Hubland Nord, University of Würzburg
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Keywords	Hilbert spaces Strong convergence Pseudomonotone operator Variational inequality Optimal control problem
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Snippet	Our aim in this paper is to introduce an extragradient-type method for solving variational inequality with uniformly continuous pseudomonotone operator. The...
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SubjectTerms	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
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Title	Convergence of an extragradient-type method for variational inequality with applications to optimal control problems
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