Applications of Mathematics, Vol. 65, No. 5, pp. 619-643, 2020

Interval matrices with Monge property

Martin Černý

Received December 23, 2019.   Published online September 4, 2020.

Abstract:  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.
Keywords:  Monge matrix; interval matrix; interval analysis; linear programming
Classification MSC:  65G99, 90C05
DOI:  10.21136/AM.2020.0370-19

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Affiliations:   Martin Černý, Charles University, Faculty of Mathematics and Physics, Department of Applied Mathematics, Malostranské nám. 2/25, 118 00 Praha 1, Czech Republic, e-mail:

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