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Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints

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Abstract

We study second-order optimality conditions for mathematical programs with equilibrium constraints (MPEC). Firstly, we improve some second-order optimality conditions for standard nonlinear programming problems using some newly discovered constraint qualifications in the literature, and apply them to MPEC. Then, we introduce some MPEC variants of these new constraint qualifications, which are all weaker than the MPEC linear independence constraint qualification, and derive several second-order optimality conditions for MPEC under the new MPEC constraint qualifications. Finally, we discuss the isolatedness of local minimizers for MPEC under very weak conditions.

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Acknowledgements

The first and second authors’ work was supported in part by NSFC Grant #11071028. The third author’s work was supported in part by NSERC. The authors are grateful to the two anonymous referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Lei Guo

  2. School of Management, Shanghai University, Shanghai, 200444, China

    Gui-Hua Lin

  3. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3P4, Canada

    Jane J. Ye

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  1. Lei Guo
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  2. Gui-Hua Lin
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  3. Jane J. Ye
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Correspondence to Gui-Hua Lin.

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Communicated by Michael Patriksson.

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Guo, L., Lin, GH. & Ye, J.J. Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints. J Optim Theory Appl 158, 33–64 (2013). https://doi.org/10.1007/s10957-012-0228-x

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