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Gap functions and error bounds for generalized vector variational inequalities

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Abstract

This paper deals with generalized vector variational inequalities. Without any scalarization approach, the gap functions and their regularized versions for generalized vector variational inequalities are first obtained. Then, in the absence of the projection operator method, some error bounds for generalized vector variational inequalities are established in terms of these regularized gap functions. Further, the results obtained in this paper are more simpler from the computational view.

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Acknowledgments

The authors would like to express their sincere thanks to the anonymous referee for many helpful comments and constructive suggestions which have contributed to the final preparation of this paper. This research was partially supported by the Basic and Advanced Research Project of CQ CSTC (Grant no: cstc2013jcyjA00003) and the National Natural Science Foundation of China (Grant no: 11301570).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Xiang-Kai Sun

  2. State Key Laboratory of Power Transmission Equipment and System Security and New Technology, College of Automation, Chongqing University, Chongqing, 400044, China

    Yi Chai

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  1. Xiang-Kai Sun
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Sun, XK., Chai, Y. Gap functions and error bounds for generalized vector variational inequalities . Optim Lett 8, 1663–1673 (2014). https://doi.org/10.1007/s11590-013-0685-7

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  • DOI: https://doi.org/10.1007/s11590-013-0685-7

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