This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Berstein, YaelLee, JonMaruri-Aguilar, HugoOnn, ShmueelRiccomagno, EvaWeismantel, RobertWynn, Henry2019-06-2820071864-7596https://doi.org/10.34657/2747https://oa.tib.eu/renate/handle/123456789/1772We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial polynomial time algorithm for arbitrary oracle-presented matroids, that makes repeated use of matroid intersection, and an algebraic algorithm for vectorial matroids. Our work is partly motivated by applications to minimum-aberration model-fitting in experimental design in statistics, which we discuss and demonstrate in detail.application/pdfeng510Report