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Image Space Analysis for Constrained Inverse Vector Variational Inequalities via Multiobjective Optimization

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Abstract

In this paper, we employ the image space analysis to study constrained inverse vector variational inequalities. First, sufficient and necessary optimality conditions for constrained inverse vector variational inequalities are established by using multiobjective optimization. A continuous nonlinear function is also introduced based on the oriented distance function and projection operator. This function is proven to be a weak separation function and a regular weak separation function under different parameter sets. Then, two alternative theorems are established, which lead directly to sufficient and necessary optimality conditions of the inverse vector variational inequalities. This provides a partial answer to an open question posed in Chen et al. (J Optim Theory Appl 166:460–479, 2015).

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Acknowledgements

The authors would like to thank the anonymous referees for their useful comments and pertinent suggestions. Moreover, the authors are grateful to Prof. Franco Giannessi and Prof. Christiane Tammer for a careful reading and helpful suggestions on an earlier draft of this manuscript, which have helped to improve the paper significantly. Also, the first author is grateful to Prof. Heinz H. Bauschke and Prof. Shawn Wang for providing excellent research facilities during his stay at Irving K. Barber School, University of British Columbia. This research was partially supported by the Natural Science Foundation of China (Nos: 11571055, 11401487), the Basic and Advanced Research Project of Chongqing (cstc2016jcyjA0239), the China Postdoctoral Science Foundation (No: 2015M582512), the Fundamental Research Funds for the Central Universities and the Grant MOST 106-2923-E-039-001-MY3.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Jiawei Chen

  2. Martin Luther University Halle-Wittenberg, Institute of Mathematics, 06099, Halle (Saale), Germany

    Elisabeth Köbis

  3. Department of Mathematics and Computer Science, Freie universität Berlin, 14195, Berlin, Germany

    Markus Köbis

  4. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Jen-Chih Yao

  5. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Jen-Chih Yao

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  1. Jiawei Chen
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  2. Elisabeth Köbis
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  3. Markus Köbis
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  4. Jen-Chih Yao
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Correspondence to Jen-Chih Yao.

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Chen, J., Köbis, E., Köbis, M. et al. Image Space Analysis for Constrained Inverse Vector Variational Inequalities via Multiobjective Optimization. J Optim Theory Appl 177, 816–834 (2018). https://doi.org/10.1007/s10957-017-1197-x

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  • DOI: https://doi.org/10.1007/s10957-017-1197-x

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