Alex Shapiro (Georgia Tech)
In the first part of the tutorial we discuss theoretical and modeling issues involved in making "optimal" decisions under conditions of uncertainty. The traditional approach is to model the underlying data process as random (stochastic) and to optimize a specified objective function on average. This raises the questions of controlling the risk, and the uncertainty with respect to the considered probability distributions themselves. In the second part of the tutorial we discuss numerical methods for solving stochastic programming problems. I will try to emphasize difficulties and limitations of different approaches and suggest important, from my point of view, open questions.