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Gap Functions and Error Bounds for Generalized Mixed Vector Equilibrium Problems

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Abstract

In this paper, we consider two classes of generalized mixed vector equilibrium problems and mixed vector equilibrium problems, and propose some gap functions by using a new method, which is different from the previously known methods used in the literature. Finally, error bounds are obtained for the underlying mixed vector equilibrium problems in terms of regularized gap functions without using projection method.

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Acknowledgments

The authors would like to thank the associated editor and the two anonymous referees for their valuable comments and suggestions, which have helped to improve the paper. This research was partially supported by the Natural Science Foundation of China (Grant: 11401487), and the Fundamental Research Funds for the Central Universities (Grants: SWU113037, XDJK2014C073).

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Authors and Affiliations

  1. Department of Mathematics, BITS-Pilani, Dubai Campus, Dubai, 345055, United Arab Emirates

    Suhel Ahmad Khan

  2. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Jia-Wei Chen

Authors
  1. Suhel Ahmad Khan
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  2. Jia-Wei Chen
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Correspondence to Suhel Ahmad Khan.

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Communicated by Suliman Saleh Al-Homidan.

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Khan, S.A., Chen, JW. Gap Functions and Error Bounds for Generalized Mixed Vector Equilibrium Problems. J Optim Theory Appl 166, 767–776 (2015). https://doi.org/10.1007/s10957-014-0683-7

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  • DOI: https://doi.org/10.1007/s10957-014-0683-7

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