A new smoothing method for mathematical programs with complementarity constraints based on logarithm-exponential function.

*(English)*Zbl 1427.90259Summary: We present a new smoothing method based on a logarithm-exponential function for mathematical program with complementarity constraints (MPCC). Different from the existing smoothing methods available in the literature, we construct an approximate smooth problem of MPCC by partly smoothing the complementarity constraints. With this new method, it is proved that the Mangasarian-Fromovitz constraint qualification holds for the approximate smooth problem. Convergence of the approximate solution sequence, generated by solving a series of smooth perturbed subproblems, is investigated. Under the weaker constraint qualification MPCC-Cone-Continuity Property, it is proved that any accumulation point of the approximate solution sequence is a M-stationary point of the original MPCC. Preliminary numerical results indicate that the developed algorithm based on the partly smoothing method is efficient, particularly in comparison with the other similar ones.

##### MSC:

90C30 | Nonlinear programming |

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

##### Software:

MacMPEC
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\textit{Y. Chen} and \textit{Z. Wan}, Math. Probl. Eng. 2018, Article ID 5056148, 11 p. (2018; Zbl 1427.90259)

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