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Exact formulas for the proximal/regular/limiting normal cone of the second-order cone complementarity set

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Abstract

The proximal, regular and limiting normal cones to the second-order cone complementarity set play important roles in studying mathematical programs with second-order cone complementarity constraints, second-order cone programs, and the second-order cone complementarity problems. It is needed in the first-order optimality conditions for mathematical programs with second-order cone complementarity constraint, the second-order subdifferential criteria in characterizing the full stability for second-order cone programs and second-order cone complementarity problems, as well as in the characterizing the pseudo-Lipschitz continuity of the solution mapping to parametric second-order cone complementarity problems. In this paper we establish explicit formulas for the proximal, regular, and limiting normal cone of the second-order cone complementarity set.

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Acknowledgments

The authors are indebted to the two anonymous reviewers for their useful comments which helped us to make the paper more concise.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada

    Jane J. Ye

  2. Department of Mathematics, School of Science, Shandong University of Technology, Zibo, 255049, People’s Republic of China

    Jinchuan Zhou

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  1. Jane J. Ye
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  2. Jinchuan Zhou
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Correspondence to Jane J. Ye.

Additional information

Jane J. Ye: The research of this author was partially supported by NSERC.

Jinchuan Zhou: This author’s work is supported by National Natural Science Foundation of China (11101248, 11271233).

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Ye, J.J., Zhou, J. Exact formulas for the proximal/regular/limiting normal cone of the second-order cone complementarity set. Math. Program. 162, 33–50 (2017). https://doi.org/10.1007/s10107-016-1027-1

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  • DOI: https://doi.org/10.1007/s10107-016-1027-1

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