Bøger i Mathematische Optimierung und Wirtschaftsmathematik | Mathematical Optimization and Economathematics serien

Anja Schedel analyzes two models in the field of algorithmic game theory which both constitute bilevel problems in networks. The first model is a game-theoretic variant of the well-known Steiner forest problem, and one is interested in an optimal sharing of the cost of the Steiner forest. The author provides (and partially exactly characterizes) network structures which allow for cost-minimal pure Nash equilibria. The second model is motivated from privatized public roads, in which private, selfishly acting firms build roads, and as compensation for their investment, are allowed to set prices for using the roads. For a basic model of this situation, the author shows existence and uniqueness of pure Nash equilibria. The existence result requires a non-standard proof approach since techniques like Kakutani's fixed point theorem cannot be applied directly.

Oleg Wilfer presents a new conjugate duality concept for geometric and cone constrained optimization problems whose objective functions are a composition of finitely many functions.

Ole Martin extends well-established techniques for the analysis of high-frequency data based on regular observations to the more general setting of asynchronous and irregular observations.

Emilia Grass develops a solution method which can provide fast and near-optimal solutions to realistic large-scale two-stage stochastic problems in disaster management.