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**Notes on convergence properties for a smoothing-regularization approach to mathematical programs with vanishing constraints.**
*(English)*
Zbl 1474.90460

Summary: We give some improved convergence results about the smoothing-regularization approach to mathematical programs with vanishing constraints (MPVC for short), which is proposed in [W. Achtziger et al., Comput. Optim. Appl. 55, No. 3, 733–767 (2013; Zbl 1291.90234)]. We show that the Mangasarian-Fromovitz constraints qualification for the smoothing-regularization problem still holds under the VC-MFCQ (see Definition 5) which is weaker than the VC-LICQ (see Definition 7) and the condition of asymptotic nondegeneracy. We also analyze the convergence behavior of the smoothing-regularization method and prove that any accumulation point of a sequence of stationary points for the smoothing-regularization problem is still strongly-stationary under the VC-MFCQ and the condition of asymptotic nondegeneracy.

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Zbl 1291.90234
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\textit{Q. Hu} et al., Abstr. Appl. Anal. 2014, Article ID 715015, 7 p. (2014; Zbl 1474.90460)

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### References:

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