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Gap Functions and Global Error Bounds for Generalized Mixed Variational Inequalities on Hadamard Manifolds

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Abstract

In this paper, a generalized mixed variational inequality on Hadamard manifolds is introduced and studied. Some gap functions for the generalized mixed variational inequality on Hadamard manifolds are obtained under suitable conditions. By using these gap functions, global error bounds for the generalized mixed variational inequality are derived on Hadamard manifolds. The main results presented in this paper generalize and improve corresponding known results.

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Acknowledgments

The authors are grateful to the editor and the referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (11171237, 11471230).

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Authors and Affiliations

  1. School of Sciences, Southwest Petroleum University, Chengdu, 610500, Sichuan, People’s Republic of China

    Xiao-bo Li & Li-wen Zhou

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Nan-jing Huang

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  1. Xiao-bo Li
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  2. Li-wen Zhou
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  3. Nan-jing Huang
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Correspondence to Nan-jing Huang.

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Li, Xb., Zhou, Lw. & Huang, Nj. Gap Functions and Global Error Bounds for Generalized Mixed Variational Inequalities on Hadamard Manifolds. J Optim Theory Appl 168, 830–849 (2016). https://doi.org/10.1007/s10957-015-0834-5

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