442 research outputs found
Nonlinear Matroid Optimization and Experimental Design
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
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