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Interval matrices with Monge property. (English) Zbl 07285949
Summary: We generalize the Monge property of real matrices for interval matrices. We define two classes of interval matrices with the Monge property – in a strong and a weak sense. We study the fundamental properties of both types. We show several different characterizations of the strong Monge property. For the weak Monge property, we give a polynomial description and several sufficient and necessary conditions. For both classes, we study closure properties. We further propose a generalization of an algorithm by Deineko and Filonenko which for a given matrix returns row and column permutations such that the permuted matrix is Monge if the permutations exist.
MSC:
65G99 Error analysis and interval analysis
90C05 Linear programming
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