Convex Techniques in Stochastic Linear Programming

We consider linear programming problems where some of the problem data are subject
to uncertainty. Such problems often times occur in operations research, for instance in the context of uncertain customer demands. We interpret uncertainty as randomness with a given probability distribution. This approach is called stochastic linear programming. We look for special cases where random problem data leads to (generalized) convex optimization problems. Then we develop mathematical theory as well as optimization algorithms to solve the resulting problems. We discuss convex duality theory and interior-point methods, a cutting plane method as well as a decomposition method for large-scale linear programming.