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

Numerical Algorithms volume 81, pages 269–291 (2019)Cite this article

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.

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Acknowledgments

The authors would like to thank Nguyen Thanh Qui and two anonymous referees for their useful comments and suggestions on the first version the paper.

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Authors and Affiliations

  1. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Phan Tu Vuong

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Phan Tu Vuong

  3. Department of Mathematics, University of Nigeria, Nsukka, Nigeria

    Yekini Shehu

  4. Institute of Mathematics, Campus Hubland Nord, University of Würzburg, Emil-Fischer-Str. 30, 97074, Würzburg, Germany

    Yekini Shehu

Authors
  1. Phan Tu Vuong
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  2. Yekini Shehu
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Correspondence to Phan Tu Vuong.

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The research of the second author is supported by the Alexander von Humboldt-Foundation.

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Vuong, P.T., Shehu, Y. Convergence of an extragradient-type method for variational inequality with applications to optimal control problems. Numer Algor 81, 269–291 (2019). https://doi.org/10.1007/s11075-018-0547-6

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  • DOI: https://doi.org/10.1007/s11075-018-0547-6

Keywords

  • Variational inequality
  • Pseudomonotone operator
  • Strong convergence
  • Hilbert spaces
  • Optimal control problem