Geodesic
Interval matrices with Monge property
Applications of Mathematics, Tome 65 (2020) no. 5, pp. 619-643.

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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.
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. http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0370-19/

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