MPCC: STRONG STABILITY OF WEAKLY NONDEGENERATE S-STATIONARY POINTS

J. Rückmann

In this paper, we consider the class of mathematical programs with complementarity constraints (MPCC). Specifically, we focus on strong stability of M- and S-stationary points for MPCC. Kojima introduced this concept for standard nonlinear optimization problems. It refers to several well-posedness properties of the underlying problem. Besides its topological definition, the challenge is to state an algebraic characterization of strong stability. We obtain such a description for S-stationary points whose components of Lagrange vectors corresponding to bi-active constraints do not mutually vanish. We call these points weakly nondegenerate. Moreover, we show that a particular constraint qualification is necessary for strong stability.
This is a joint work with Harald Günzel (RWTH Aachen University, Germany) and Daniel Hernandez Escobar (Uppsala University, Sweden).

Palabras clave: Mathematical programs with complementarity constraints (MPCC), M- and S-stationarity, strong stability, algebraic characterization, Generalized Mangasarian-Fromovitz constraint qualification

Optimización Continua II
10 de junio de 2025  15:30
MR 3

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