Notes on Convergence Properties for a Smoothing-Regularization Approach to Mathematical Programs with Vanishing Constraints

Qingjie Hu, Yu Chen, Zhibin Zhu and Bishan Zhang

Abstract and Applied Analysis, 2014, vol. 2014, 1-7

Abstract:

We give some improved convergence results about the smoothing-regularization approach to mathematical programs with vanishing constraints (MPVC for short), which is proposed in Achtziger et al. (2013). 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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:715015

DOI: 10.1155/2014/715015

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