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arXiv · 0707.4618

Nonlinear Matroid Optimization and Experimental Design

Yael Berstein·Jon Lee·Hugo Maruri-Aguilar·Shmuel Onn·Eva Riccomagno·Robert Weismantel·Henry Wynn
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Abstract

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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BibTeXRIS

Yael Berstein, Jon Lee, Hugo Maruri-Aguilar, Shmuel Onn, Eva Riccomagno, Robert Weismantel, Henry Wynn. 2007-07-31. Nonlinear Matroid Optimization and Experimental Design. https://arxiv.org/abs/0707.4618

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