Orateur
Description
Two-stage stochastic programs with finite support are a fundamental tool for decision-making under uncertainty. However, their computational tractability is often limited by the number of scenarios considered. To address this issue, scenario clustering methods have been proposed to reduce the problem size while preserving the essential characteristics of the uncertain parameters that drive the decision-making. In this work, we propose a novel matrix-theoretic perspective on scenario clustering for two-stage stochastic programs. We show that any clustering-based approach can be represented as an inner and/or an outer approximation of the original problem obtained by taking advantage of a clustering matrix. This unified framework provides an optimization-oriented understanding of the impact of clustering on the optimization model and paves the way for the development of new computational approaches. We explore research directions that arise from our observations. These research directions include the development of novel clustering methods, the integration of advanced matrix decomposition techniques, and the extension of our framework to broader classes of optimization problems.
