Title: Introduction to the special issue on computational optimization under uncertainty
Abstract: This special issue on Computational Optimization under Uncertainty was initiated during the 11th Conference on Stochastic Programming which was held at the University of Vienna in August 2007. A carefully selected range of papers has been chosen for publication in this issue. The aim is to provide an up-to-date overview of state-of-the-art stochastic programming techniques and applications. Most contributions consider the valuable but more challenging multi-stage case. Both contributions improving computational solutions of the optimization programs in general, as well as a set of specific applications from different management areas are covered. The first part of this issue is dedicated to numerical solution frameworks and approaches for multi-stage stochastic programs. In the first paper, Holger Heitsch and Werner Romisch tackle the problem of calculating an optimal reduction of multi-stage scenarios trees to allow for more tractable computational solutions once the underlying scenario tree is huge. In contrast to the much simpler two-stage case of scenario (tree) reduction, themulti-stage case is handled by incorporating the filtration distance. An algorithm is presented, which aims at fulfilling predefined error tolerances. Jacek Gondzio and Andreas Grothey examine special structures of optimization problems, and present the implementation of the software library OOPS, which is an object oriented parallel solver using primal–dual interior point methods to exploit special matrix structures, which are often prevalent in multi-stage stochastic programming problems.