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IMI/Publicaţii/CSJM/Ediţii/CSJM v.12, n.1 (34), 2004/

On quasistability of a vector combinatorial problem with Σ-MINMAX and Σ-MINMIN partial criteria

Authors: Vladimir A. Emelichev, Kirill G. Kuzmin, Andrey M. Leonovich
Keywords: Vector trajectorial problem, the Pareto set, quasi-stability.

Abstract

We consider one type of stability (quasistability) of a vector combinatorial problem of finding the Pareto set. Under quasistability we understand a discrete analogue of lower semicontinuity by Hausdorff of the many-valued mapping, which defines the Pareto choice function. A vector problem on a system of subsets of a finite set (trajectorial problem) with non-linear partial criteria is in focus. Two necessary and sufficient conditions for stability of this problem are proved. Mathematics Subject Classification: 2000, 90C10, 90C05, 90C29, 90C31

V. A. Emelichev, K. G. Kuzmin, A. M. Leonovich
Belorussian State University,
Mechanics-Mathematics Department,
ave. Fr. Skoriny, 4, Minsk, 220050, Belarus.
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