Título: Strong stability of C-stationary points for mathematical programs with complementarity constraints
Ponente: Jan-J. Rückmann (University of Bergen, Norway)
Fecha y hora: 10/09/2024, 12:30
Inscripción online (cierre 30 minutos antes del inicio): https://forms.gle/2fJouyhen2HYmzxj8
Lugar: Sala de Seminarios (UMH Campus de Elche, Edificio Torretamarit) y online
Organizador: Juan Parra López
Abstract:
We consider the class of mathematical programs with complementarity constraints (MPCC). There are several well-known real-life applications of this optimization model. In the following we are concerned with an important sensitivity property of solutions of MPCC, namely, the strong stability of C-stationary points. Among different stationarity concepts for MPCC the so-called C-stationarity fulfills certain topological properties generalizing features from Morse Theory.
The concept of strong stability was originally introduced by Kojima for standard – in general, non-convex – optimization problems. It refers to several well-posedness properties of the underlying problem such as existence, uniqueness and continuous dependance on the data. Besides its topological definition, the challenge consists in stating an algebraic characterization of strong stability. We deliver such a description for those C-stationary points whose components of Lagrange vectors corresponding to bi-active constraints do not vanish at the same time. Furthermore, we show that a particular constraint qualification is necessary for strong stability.
This talk is based on joint works with
- DANIEL HERNANDEZ ESCOBAR (University of Uppsala, Sweden)
- HARALD GÜNZEL (RWTH Aachen University, Germany)