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Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints

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Abstract.

Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced under fairly general conditions other than strict complementarity or the linear independence constraint qualification for MPEC (MPEC-LICQ). It is shown that every limit point of the generated sequence is a strong stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a point with certain stationarity can be obtained. Preliminary numerical results are reported, which include a case analyzed by Leyffer for which the penalty interior-point algorithm failed to find a stationary point.

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Authors and Affiliations

  1. Singapore-MIT Alliance, National University of Singapore and Department of Applied Mathematics, Hebei University of Technology, Tianjin, China

    Xinwei Liu & Jie Sun

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  1. Xinwei Liu
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  2. Jie Sun
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Correspondence to Jie Sun.

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Mathematics Subject Classification (1991):90C30, 90C33, 90C55, 49M37, 65K10

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Liu, X., Sun, J. Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints. Math. Program., Ser. A 101, 231–261 (2004). https://doi.org/10.1007/s10107-004-0543-6

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  • DOI: https://doi.org/10.1007/s10107-004-0543-6

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