joint work with Alexandra Schwartz
Multi-leader-follower games (MLFGs) can be seen as an hierarchical extension of Nash equilibrium problems. By now, the analysis of the latter is well-known and well-understood even in infinite dimensions. While the analysis of MLFGs in finite dimensions is restricted to special cases, the analysis in function spaces is still in its infancy. Therefore, the talk focuses on linear-quadratic MLFGs in Hilbert spaces and their corresponding equilibrium problems with complementarity constraints (EPCCs). By considering relaxed equilibrium problems, we derive a novel equilibrium concept for MLFGs.
joint work with Simone Sagratella
Semi-infinite programs (SIPs) can be formulated as generalized Nash games (GNEPs) with a peculiar structure under mild assumptions. Pairing this structure with a penalization scheme for GNEPs leads to methods for SIPs. A projected subgradient method for nonsmooth optimization and a subgradient method for saddlepoints are adapted to our framework, providing two kinds of the basic iteration for the penalty scheme. Beyond comparing the two algorithms, these results and algorithms are exploited to deal with uncertainty and analyse robustness in portfolio selection and production planning.