Abstract
In this paper, by using scalarization techniques and a minimax strategy, error bound results in terms of gap functions for a generalized mixed vector equilibrium problem are established, where the solutions for vector problems may be general sets under natural assumptions, but are not limited to singletons. The other essentially equivalent approach via a separation principle is analyzed. Special cases to the classical vector equilibrium problem and vector variational inequality are also discussed.
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Acknowledgements
The authors gratefully thank the anonymous referees and the associate editor Professor Xin-Min Yang for their constructive suggestions and comments, which helped to improve the paper.
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This research was supported by the National Natural Science Foundation of China (Nos. 11301567 and 11571055) and the Fundamental Research Funds for the Central Universities (No. 106112015CDJXY100002).
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Chen, CR., Chen, X., Wei, HZ. et al. Error Bounds for Generalized Mixed Vector Equilibrium Problems via a Minimax Strategy. J. Oper. Res. Soc. China 6, 317–331 (2018). https://doi.org/10.1007/s40305-017-0169-z
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DOI: https://doi.org/10.1007/s40305-017-0169-z