Mathematical programs with vanishing constraints: constraint qualifications,their applications,and a new regularization method |
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Authors: | J-P Dussault M Haddou |
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Institution: | 1. Département d'Informatique, faculté des Sciences, Université de Sherbrooke, Sherbrooke, Canada;2. Univ Rennes, INSA Rennes, CNRS, IRMAR - UMR 6625, Rennes, France |
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Abstract: | ABSTRACTWe 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. |
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Keywords: | Non-linear programming MPCC MPEC MPVC relaxation methods |
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