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Characterization of weakly sharp solutions of a variational inequality by its primal gap function

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Abstract

Our aim is to study weakly sharp solutions of a variational inequality in terms of its primal gap function \(g\). We discuss sufficient conditions for the Lipschitz continuity and subdifferentiability of the primal gap function. Several sufficient conditions for the relevant mapping to be constant on the solutions have also been obtained. Based on these, we characterize the weak sharpness of the solutions of a variational inequality by \(g\). Some finite convergence results of algorithms for solving variational inequality problems are also included.

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Acknowledgments

We thank the anonymous referees for their valuable comments, suggestions and supports.

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Author notes

  1. Yina Liu

    Present address: Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Suzhou, Jiangsu, 215123, China

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX, UK

    Yina Liu

  2. Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Suzhou, Jiangsu, 215123, China

    Zili Wu

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  1. Yina Liu
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Correspondence to Zili Wu.

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Liu, Y., Wu, Z. Characterization of weakly sharp solutions of a variational inequality by its primal gap function. Optim Lett 10, 563–576 (2016). https://doi.org/10.1007/s11590-015-0882-7

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  • DOI: https://doi.org/10.1007/s11590-015-0882-7

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