Abstract
This paper considers the problem of minimizing the ordered median function of finitely many rational functions over compact semi-algebraic sets. Ordered median of rational functions are not, in general, neither rational functions nor the supremum of rational functions.We prove that the problem can be transformed into a new problem embedded in a higher dimension space where it admits a convenient representation. This reformulation admits a hierarchy of SDP relaxations that approximates, up to any degree of accuracy, the optimal value of those problems. We apply this general framework to a broad family of continuous location problems solving some difficult problems.
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