Nonlinear Matroid Optimization and Experimental Design

Details Nonlinear Matroid Optimization and Experimental Design Nonlinear Matroid Optimization and Experimental Design

2007-07-31

arxiv.org/abs/0707.4618v1

SIAM Journal on Discrete Mathematics, 22:901--919, 2008

Mathematics

Combinatorics

Scientific paper

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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