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Strong convergence result for monotone variational inequalities

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Abstract

Our aim in this paper is to study strong convergence results for L-Lipschitz continuous monotone variational inequality but L is unknown using a combination of subgradient extra-gradient method and viscosity approximation method with adoption of Armijo-like step size rule in infinite dimensional real Hilbert spaces. Our results are obtained under mild conditions on the iterative parameters. We apply our result to nonlinear Hammerstein integral equations and finally provide some numerical experiments to illustrate our proposed algorithm.

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Authors and Affiliations

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

    Yekini Shehu

  2. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, WI, USA

    Olaniyi S. Iyiola

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  1. Yekini Shehu
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  2. Olaniyi S. Iyiola
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Correspondence to Yekini Shehu.

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The First Author is currently an Alexander von Humboldt Postdoctoral Fellow at the Institute of Mathematics, University of Wurzburg, Germany.

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Shehu, Y., Iyiola, O.S. Strong convergence result for monotone variational inequalities. Numer Algor 76, 259–282 (2017). https://doi.org/10.1007/s11075-016-0253-1

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