Stochastic programming addresses optimization under uncertainty if distributional information is available for the unknown data. Depending on when realizations of uncertain data are known and on how this interacts with decision making over time, there are different model frameworks in stochastic programming, e. g., one-stage, two-stage, or multi-stage models. Selection and placement (in the objective or the constraints) of the statistical parameters according to which relevant random variables are to be evaluated is another important issue. This allows to express perceptions such as reliability, risk neutrality, or risk aversion. Finally, the nature of the initial uncertain optimization problem (finite- or infinitedimensional, linear or non linear, with or without integer variables) has crucial impact on the resulting stochastic programming model. These ascpects lead to a wide variety of models and mathematical techniques for their analysis and algorithmic treatment. ln the talk, we focus on the two-stage modelframewerk of mutual interaction of decisions and observations. As stated in the title, this includes models, theory, and algorithms for the two-stage (or recourse) framework. The presentation includes both recent results and departure points for future research.

Referent: Prof. Dr. Rüdiger Schultz, Universität Duisburg-Essen