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Some properties of regularization and penalization schemes for MPECs. (English) Zbl 1097.90054

Summary: Some properties of regularized and penalized nonlinear programming formulations of mathematical programs with equilibrium constraints (MPECs) are described. The focus is on the properties of these formulations near a local solution of the MPEC at which strong stationarity and a second-order sufficient condition are satisfied. In the regularized formulations, the complementarity condition is replaced by a constraint involving a positive parameter that can be decreased to zero. In the penalized formulation, the complementarity constraint appears as a penalty term in the objective. The existence and uniqueness of solutions for these formulations are investigated, and estimates are obtained for the distance of these solutions to the MPEC solution under various assumptions.

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
91A40 Other game-theoretic models

Software:

MacMPEC
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Full Text: DOI

References:

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