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- ItemNonlinear matroid optimization and experimental design(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2007) Berstein, Yael; Lee, Jon; Maruri-Aguilar, Hugo; Onn, Shmueel; Riccomagno, Eva; Weismantel, Robert; Wynn, HenryWe 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.