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A smoothing Newton method for mathematical programs governed by second-order cone constrained generalized equations

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Abstract

In this paper, we consider a class of mathematical programs governed by second-order cone constrained parameterized generalized equations. We reformulate the necessary optimality conditions as a system of nonsmooth equations under linear independence constraint qualification and the strict complementarity condition. A set of second order sufficient conditions is proposed, which is proved to be sufficient for the second order growth of the stationary point. The smoothing Newton method in [40] is employed to solve the system of nonsmooth equations whose strongly BD-regularity at a solution point is demonstrated under the second order sufficient conditions. Several illustrative examples are provided and discussed.

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Authors and Affiliations

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

    Jia Wu, Liwei Zhang & Yi Zhang

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  1. Jia Wu
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  2. Liwei Zhang
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  3. Yi Zhang
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Correspondence to Jia Wu.

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The research is supported by the National Natural Science Foundation of China under project No. 11071029 and the Fundamental Research Funds for the Central Universities.

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Wu, J., Zhang, L. & Zhang, Y. A smoothing Newton method for mathematical programs governed by second-order cone constrained generalized equations. J Glob Optim 55, 359–385 (2013). https://doi.org/10.1007/s10898-012-9880-9

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  • DOI: https://doi.org/10.1007/s10898-012-9880-9

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