Notes on convergence properties for a smoothing-regularization approach to mathematical programs with vanishing constraints (Q1724802)

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 [\textit{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.