Mathematical programs with vanishing constraints: constraint qualifications, their applications, and a new regularization method. (4th March 2019)

• Record Type: Journal Article
• Authors: Dussault, J.-P.; Haddou, M.; Migot, T.
• Is Part Of: Optimization. Volume 68:Number 2/3(2019)
• Page Start: 509
• Page End: 538
• Publication Date: 2019-03-04
• Subjects: Non-linear programming -- MPCC -- MPEC -- MPVC -- relaxation methods; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1542531
• Languages: English
• ISSNs: 0233-1934

Abstract

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. 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.