2007, Berstein, Yael, Lee, Jon, Maruri-Aguilar, Hugo, Onn, Shmueel, Riccomagno, Eva, Weismantel, Robert, Wynn, Henry

We 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.