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Abstract and Applied Analysis
Volume 2014, Article ID 715015, 7 pages
http://dx.doi.org/10.1155/2014/715015
Research Article

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

1School of Mathematics and Computing Science, Guilin University of Electronic Technology, 541004 Guilin, China
2School of Mathematics and Statistics, Central South University, 410083 Changsha, China

Received 24 June 2014; Accepted 29 July 2014; Published 1 September 2014

Academic Editor: Yunhai Xiao

Copyright © 2014 Qingjie Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.