Strong Stability and Stationarity for Mathematical Problems with Complementarity Constraints

J. Rückmann

The topic of this lecture are mathematical problems with complementarity constraints (MPCC). In particular, we discuss (strong and weak) stability properties of different types of stationary points of MPCC, where perturbations up to second order are taken into account. Here, well-posedness properties as existence, uniqueness and continuous dependence on the perturbations of a stationary point are discussed. The concept of strong stability was originally introduced for standard nonlinear optimization problems which do not include complementarity constraints as in MPCC. In the context of stability a corresponding constraint qualification is also discussed. This lecture is based on joint works with Harald Günzel (RWTH Aachen University, Germany) and Daniel Hernandez Escobar (University of Uppsala, Sweden)

Keywords: Strong stability, Stationarity, Well-posedness, Mathematical programs with complementarity constraints

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