Mathematical Programs with Vanishing Constraints: Constraint Qualifications, their Applications and a New Regularization Method

Abstract : 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. We obtain the new MPVC-wGCQ and prove that it is the weakest constraint qualification for MPVC. We also introduce a new constraint qualification, MPVC-CRSC, that is sufficient to guarantee the convergence of the new method. Under this weak condition, we also provide an error bound and an exact penalty result for the MPVC.
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Submitted on : Monday, February 5, 2018 - 6:04:15 PM
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Jean-Pierre Dussault, Mounir Haddou, Tangi Migot. Mathematical Programs with Vanishing Constraints: Constraint Qualifications, their Applications and a New Regularization Method. Optimization, Taylor & Francis, 2019, 68 (2-3), pp.509-538. ⟨10.1080/02331934.2018.1542531⟩. ⟨hal-01701461⟩

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