Geodesic
On the radii of stability, quasistability and steadiness of a vector trajectory problem of lexicographic optimization
Diskretnaya Matematika, Tome 10 (1998) no. 1, pp. 20-27
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We consider a multicriteria problem on lexicographic optimization on a system of subsets of a finite set (a trajectory problem) with a vector criterion function consisting of linear criteria. We investigate different types of steadiness of the lexicographic set under small variations of parameters of the criterion functions. We give formulae for computing the radii of steadiness, quasi-steadiness, and stability in the case of Chebyshev norm in the space of perturbed parameters.The research was supported by the Foundation for Basic Research of the Byelarussian Republic, grants F 23–70 and F 95–70, the International Soros Education Program in Exact Sciences and Foundation DAAD (for the first author). 
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     author = {V. A. Emelichev and R. A. Berdysheva},
     title = {On the radii of stability, quasistability and steadiness of a vector trajectory problem of lexicographic optimization},
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     pages = {20--27},
     year = {1998},
     volume = {10},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1998_10_1_a2/}
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V. A. Emelichev; R. A. Berdysheva. On the radii of stability, quasistability and steadiness of a vector trajectory problem of lexicographic optimization. Diskretnaya Matematika, Tome 10 (1998) no. 1, pp. 20-27. http://geodesic.mathdoc.fr/item/DM_1998_10_1_a2/