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Bilevel invex equilibrium problems with applications

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Abstract

In this paper, bilevel invex equilibrium problems of Hartman-Stampacchia type and Minty type [resp., in short, (HSBEP) and (MBEP)] are firstly introduced in finite Euclidean spaces. The relationships between (HSBEP) and (MBEP) are presented under some suitable conditions. By using fixed point technique, the nonemptiness and compactness of solution sets to (HSBEP) and (MBEP) are established under the invexity, respectively. As applications, we investigate the existence of solution and the behavior of solution set to the bilevel pseudomonotone variational inequalities of [Anh et al. J Glob Optim 2012, doi:10.1007/s10898-012-9870-y] and the solvability of minimization problem with variational inequality constraint.

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Acknowledgments

The authors are indebted to the referees and the associate editor for their insightful and pertinent comments on an earlier version of the work. The first author would like to gratefully thank Professor Heinz H. Bauschke and Shawn Wang, Mathematics, Irving K. Barber School, UBC Okanagan, Kelowna, British Columbia, Canada, for their hospitality and providing excellent research facilities.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, People’s Republic of China

    Jia-wei Chen & Zhongping Wan

  2. School of Information and Mathematics, Yangtze University, Jingzhou, 434023, Hubei, People’s Republic of China

    Jia-wei Chen

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

    Yun-Zhi Zou

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  1. Jia-wei Chen
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  2. Zhongping Wan
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  3. Yun-Zhi Zou
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Correspondence to Jia-wei Chen.

Additional information

This work was supported by the Natural Science Foundation of China (71171150), the Academic Award for Excellent Ph.D. Candidates Funded by Wuhan University and the Fundamental Research Fund for the Central Universities (No. 201120102020004) and the Ph.D short-time mobility program by Wuhan University.

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Chen, Jw., Wan, Z. & Zou, YZ. Bilevel invex equilibrium problems with applications. Optim Lett 8, 447–461 (2014). https://doi.org/10.1007/s11590-012-0588-z

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  • DOI: https://doi.org/10.1007/s11590-012-0588-z

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