Geodesic
Interval matrices with Monge property
Applications of Mathematics, Tome 65 (2020) no. 5, pp. 619-643 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2020.0370-19
Classification : 65G99, 90C05
Keywords: Monge matrix; interval matrix; interval analysis; linear programming 
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     title = {Interval matrices with {Monge} property},
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Černý, Martin. Interval matrices with Monge property. Applications of Mathematics, Tome 65 (2020) no. 5, pp. 619-643. doi: 10.21136/AM.2020.0370-19

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