A globally convergent algorithm for MPCC.

*(English)*Zbl 1326.49050Summary: We propose a penalty formulation based on the new regularization scheme for Mathematical Programs with Complementarity Constraints (MPCCs). We present an active set method which solves a sequence of penalty-regularized problems. We study global convergence properties of the method under the MPCC-linear independence constraint qualification. In particular, any accumulation point of the generated iterates is a strong stationary point if the penalty parameter is bounded. Otherwise, the convergence to points having a certain stationarity property is established. A strategy for updating the penalty parameter is proposed and numerical results on a collection of test problems are reported.

##### MSC:

49M37 | Numerical methods based on nonlinear programming |

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |

90C30 | Nonlinear programming |

90C52 | Methods of reduced gradient type |

65K05 | Numerical mathematical programming methods |

##### Keywords:

nonlinear programming; complementarity constraints; regularization; penalization; global convergence
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\textit{A. Kadrani} et al., EURO J. Comput. Optim. 3, No. 3, 263--296 (2015; Zbl 1326.49050)

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