English

Nonlinear Matroid Optimization and Experimental Design

Combinatorics 2008-07-24 v1 Computational Complexity Discrete Mathematics Optimization and Control

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.

Keywords

Cite

@article{arxiv.0707.4618,
  title  = {Nonlinear Matroid Optimization and Experimental Design},
  author = {Yael Berstein and Jon Lee and Hugo Maruri-Aguilar and Shmuel Onn and Eva Riccomagno and Robert Weismantel and Henry Wynn},
  journal= {arXiv preprint arXiv:0707.4618},
  year   = {2008}
}
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