Geodesic
A general approach to studying the stability of a~Pareto optimal solution of a~vector integer linear programming problem
Diskretnaya Matematika, Tome 19 (2007) no. 3, pp. 79-83

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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. 
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     author = {V. A. Emelichev and K. G. Kuz'min},
     title = {A general approach to studying the stability of {a~Pareto} optimal solution of a~vector integer linear programming problem},
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     pages = {79--83},
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V. A. Emelichev; K. G. Kuz'min. A general approach to studying the stability of a~Pareto optimal solution of a~vector integer linear programming problem. Diskretnaya Matematika, Tome 19 (2007) no. 3, pp. 79-83. http://geodesic.mathdoc.fr/item/DM_2007_19_3_a5/