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Extension of forward-reflected-backward method to non-convex mixed variational inequalities

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Abstract

This paper presents a modification of a recently studied forward-reflected-backward splitting method to solve non-convex mixed variational inequalities. We give global convergence results and nonasymptotic O(1/k) rate of convergence of the proposed method under some appropriate conditions and present some numerical illustrations, one of which is derived from oligopolistic equilibrium problems, to show the efficiency of our proposed method.

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Acknowledgements

The authors are grateful to the associate editor and the anonymous referee for their insightful comments and suggestions which have improved greatly on the earlier version of the manuscript.

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Authors and Affiliations

  1. School of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, 2050, South Africa

    Chinedu Izuchukwu & Chibueze C. Okeke

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yekini Shehu

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  1. Chinedu Izuchukwu
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  2. Yekini Shehu
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Correspondence to Yekini Shehu.

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Izuchukwu, C., Shehu, Y. & Okeke, C.C. Extension of forward-reflected-backward method to non-convex mixed variational inequalities. J Glob Optim 86, 123–140 (2023). https://doi.org/10.1007/s10898-022-01253-w

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  • DOI: https://doi.org/10.1007/s10898-022-01253-w

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