2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165507We 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.CombinatoricsComputational ComplexityDiscrete MathematicsOptimization and Control90C11, 52B55, 90B06, 68R05, 15A39, 62H17text