MPCC: on necessary conditions for the strong stability of C-stationary points. (4th March 2019)

• Record Type: Journal Article
• Authors: Hernández Escobar, Daniel; Rückmann, Jan-J.
• Is Part Of: Optimization. Volume 68:Number 2/3(2019)
• Page Start: 593
• Page End: 613
• Publication Date: 2019-03-04
• Subjects: Mathematical programs with complementarity constraints -- C-stationary point -- strong stability -- Mangasarian-Fromovitz-type constraint qualification -- necessary condition; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1584800
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We consider the concept of strongly stable C-stationary points for mathematical programs with complementarity constraints. The original concept of strong stability was introduced by Kojima for standard optimization programs. Adapted to our context, it refers to the local existence and uniqueness of a C-stationary point for each sufficiently small perturbed problem. The goal of this paper is to discuss a Mangasarian-Fromovitz-type constraint qualification and, mainly, provide two conditions which are necessary for strong stability; one is another constraint qualification and the second one refers to bounds on the number of active constraints at the point under consideration.