Least majorized elements and generalized polymatroids

Least majorized elements and generalized polymatroids

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Article ID: iaor20041746
Country: United States
Volume: 20
Issue: 3
Start Page Number: 583
End Page Number: 589
Publication Date: Aug 1995
Journal: Mathematics of Operations Research
Authors:
Abstract:

We prove that a bounded generalized polymatroid has a least weakly submajorized (supermajorized) vector. Such a vector simultaneously minimizes every nondecreasing (nonincreasing), symmetric and quasi-convex function defined on the generalized polymatroid. The same result holds also for the set of integer vectors of a bounded integral generalized polymatroid. We then extend these results to more general sets, and discuss several computational aspects.

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