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On the coderivative of the solution mapping to a second-order cone constrained parametric variational inequality

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Abstract

The explicit representation of Mordukhovich coderivative of a solution mapping to a second-order cone constrained parametric variational inequality is established by the reduction approach. The result obtained is used to obtain a necessary and sufficient condition for the Lipschitz-like property of the solution mapping to the parametric variational inequality and global optimality conditions for a bilevel programming with a second-order cone constrained lower level problem.

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Acknowledgments

The authors are grateful to referees and an editor for the constructive comments which significantly helped improve the quality of the paper.

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Authors and Affiliations

  1. Research Center of Information and Control, Dalian University of Technology, Dalian , 116024, China

    Jie Zhang

  2. Institute of ORCT, School of Mathematical Sciences, Dalian University of Technology, Dalian , 116024, China

    Yu-xin Li & Li-wei Zhang

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  1. Jie Zhang
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  2. Yu-xin Li
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  3. Li-wei Zhang
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Correspondence to Jie Zhang.

Additional information

Supported by the National Natural Science Foundation of China under Project Nos. 11201210 and 11171138 and Scientific Research Fund of Liaoning Provincial Education Department under Project No. L2012385.

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Zhang, J., Li, Yx. & Zhang, Lw. On the coderivative of the solution mapping to a second-order cone constrained parametric variational inequality. J Glob Optim 61, 379–396 (2015). https://doi.org/10.1007/s10898-014-0181-3

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  • DOI: https://doi.org/10.1007/s10898-014-0181-3

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