MPCC: strongly stable C-stationary points when the number of active constraints is n + 1

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.

Keywords:

• Mathematical problems with complementarity constraints
• strong stability
• C-stationary point
• Mangasarian-Fromovitz condition
• algebraic characterization

Disclosure statement

No potential conflict of interest was reported by the authors.