Nonlinear Optimization over a Weighted Independence System
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Computation in multicriteria matroid optimization
Journal of Experimental Algorithmics (JEA)
Approximate Nonlinear Optimization over Weighted Independence Systems
SIAM Journal on Discrete Mathematics
Concentration inequalities for nonlinear matroid intersection
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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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 multicriteria 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.