Numer Algor https://doi.org/10.1007/s11075-018-0547-6 ORIGINAL PAPER Convergence of an extragradient-type method for variational inequality with applications to optimal control problems 1,2 3,4 Phan Tu Vuong · Yekini Shehu Received: 28 December 2017 / Accepted: 9 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract Our aim in this paper is to introduce an extragradient-type method for solving variational inequality with uniformly continuous pseudomonotone opera- tor. 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 assump- tions. Finally, we give numerical implementations of our results for optimal control problems governed by ordinary differential equations. Keywords Variational inequality · Pseudomonotone operator · Strong convergence · Hilbert spaces · Optimal control problem The research of the second author is supported by the Alexander von Humboldt-Foundation. Yekini Shehu firstname.lastname@example.org Phan Tu Vuong email@example.com Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam Department of Mathematics, University of Nigeria, Nsukka, Nigeria Institute of Mathematics, Campus
Numerical Algorithms – Springer Journals
Published: May 28, 2018
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