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Mathematical programs with vanishing constraints: constraint qualifications, their applications, and a new regularization method

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posted on 2018-11-20, 01:24 authored by J.-P. Dussault, M. Haddou, T. Migot

We propose a new family of relaxation schemes for mathematical programs with vanishing constraints that extend the relaxation of Hoheisel, Kanzow & Schwartz from 2012. We discuss the properties of the sequence of relaxed non-linear programs as well as stationary properties of limiting points. Our relaxation schemes have the desired property of converging to an M-stationary point. A main advantage of this new method is to converge to an S-stationary point satisfying MPVC-LICQ for a large class of problem. We also study MPVC constraint qualification connected to this study and prove convergence of the method under the new MPVC-CRSC. Additionally, we obtain the new MPVC-wGCQ and prove that it is the weakest MPVC constraint qualification.

Funding

This research was partially supported by NSERC grant. This research was also partially supported by a French grant from ‘l'Ecole des Docteurs de l'UBL’ and ‘le Conseil Régional de Bretagne’.

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