MPCC: strongly stable C-stationary points when the number of active constraints is n + 1. (3rd May 2020)

• Record Type: Journal Article
• Authors: Hernández Escobar, Daniel; Rückmann, Jan-J.
• Is Part Of: Optimization. Volume 69:Number 5(2020)
• Page Start: 1039
• Page End: 1067
• Publication Date: 2020-05-03
• Subjects: Mathematical problems with complementarity constraints -- strong stability -- C-stationary point -- Mangasarian-Fromovitz condition -- algebraic characterization; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1671385
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We consider the class of mathematical problems with complementarity constraints (MPCC) and apply Kojima's concept of strongly stable stationary points (originally introduced for a standard optimization problem) to C-stationary points of MPCC under certain assumptions. This concept refers to local existence and uniqueness of a stationary point for each sufficiently small perturbed problem. Assuming that the number of active constraints is n +1 and an appropriate constraint qualification holds at the considered point, the goal of this paper is twofold: For MPCC we will present necessary conditions for strong stability as well as equivalent algebraic characterizations for this topological concept.