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An inexact Newton method for stationary points of mathematical programs constrained by parameterized quasi-variational inequalities

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Abstract

In this paper, we propose a numerical method for solving the stationary points of mathematical programs constrained by parameterized quasi-variational inequalities. The necessary optimality conditions (stationary conditions in the sense of Mordukhovich) for the optimization problem are reformulated as a system of nonsmooth equations without the strict complementarity condition and an inexact Newton method is constructed to find its solutions. The local convergence of the inexact Newton method is guaranteed under second order sufficient conditions and linear independence constraint qualification. Several illustrative examples are provided.

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Authors and Affiliations

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

    Jia Wu & Liwei Zhang

  2. Department of Mathematics, School of Science, East China University of Science and Technology, Shanghai, 200237, China

    Yi Zhang

Authors
  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.

Additional information

The research is supported by the National Natural Science Foundation of China under project No. 11301049, No. 91130007, No. 91330206, No. 11401210, Project funded by China Postdoctoral Science Foundation (2013M541217) and the Fundamental Research Funds for the Central Universities(222201314037).

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Wu, J., Zhang, L. & Zhang, Y. An inexact Newton method for stationary points of mathematical programs constrained by parameterized quasi-variational inequalities. Numer Algor 69, 713–735 (2015). https://doi.org/10.1007/s11075-014-9922-0

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