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A general approach to studying the stability of a Pareto optimal solution of a vector integer linear programming problem. (English. Russian original) Zbl 1278.90268
Discrete Math. Appl. 17, No. 4, 349-354 (2007); translation from Diskretn. Mat. 19, No. 3, 79-83 (2007).
Summary: We consider a multicriteria integer linear programming problem with a finite set of admissible solutions. With the use of Minkowski-Mahler inequality, we obtain a bound for the domain in the space of parameters of the problem equipped with some norm where the Pareto optimality of the solution is still retained. In the case of a monotone norm, we give a formula for the stability radius of the solution. As a corollary we obtain the formula for the stability radius in the case of the Hölder norm and, in particular, the Chebyshev norm in the space of parameters of a vector criterion.

MSC:
90C10 Integer programming
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