Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

With geometric modeling techniques, one can represent the feasible solutions of problems in operations research as objects in high-dimensional space. The properties of these objects reveal information about the underlying problems and lead to algorithms. We model an application in the consolidation of farmland and private forests as a clustering problem where the clusters have to adhere to prescribed cluster sizes. In this approach, we connect least-squares assignments, cell complexes, and the studies of polyhedra. The devised methods lead to generalizations of the classical k-means algorithm and algorithms for soft-margin separation in general data analysis tasks. Further, we report on how these results were implemented in practice.