Geodesic
On comparison of approximate solutions in vector optimization problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1790-1801 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of comparison of approximations (approximate solutions to a vector optimization problem) obtained using different numerical methods is considered. In the absence of a priori information about the set of weakly efficient vectors, a scalar function is introduced that enables pair-wise comparison of approximations and establishes a binary preference relation according to which the approximations close (in the sense of the Hausdorff distance) to the set containing all possible efficient vectors are preferable to other approximations. 
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     title = {On comparison of approximate solutions in vector optimization problems},
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Ya. I. Rabinovich. On comparison of approximate solutions in vector optimization problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1790-1801. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a7/

[1] Germeier Yu. B., Vvedenie v teoriyu issledovaniya operatsii, Nauka, M., 1971 | MR

[2] Rabinovich Ya. I., “Postroenie mnozhestva effektivnykh vektorov metodom $\varepsilon$-vozmuschenii”, Zh. vychisl. matem. i matem. fiz., 45:5 (2005), 824–845 | MR | Zbl

[3] Fedorov V. V., Chislennye metody maksimina, Nauka, M., 1979 | MR

[4] Stenli R., Perechislitelnaya kombinatorika, Mir, M., 1990 | MR