Abstract
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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References
Yu. B. Germeier, Introduction to Operations Research (Nauka, Moscow, 1971) [in Russian].
Ya. I. Rabinovich, “Constructing the Set of Effective Vectors by the Method of ɛ-Perturbations,” Zh. Vychisl. Mat. Mat. Fiz. 45, 824–845 (2005) [Comput. Math. Math. Phys. 45, 794–815 (2005)].
V. V. Fedorov, Numerical Maximin Methods (Nauka, Moscow, 1979) [in Russian].
R. Stanley, Enumerative Combinatorics (Cambridge University Press, Cambridge 1997–1999; Mir, Moscow, 1990).
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Original Russian Text © Ya.I. Rabinovich, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 10, pp. 1790–1801.
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Rabinovich, Y.I. On comparison of approximate solutions in vector optimization problems. Comput. Math. and Math. Phys. 46, 1705–1716 (2006). https://doi.org/10.1134/S0965542506100083
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DOI: https://doi.org/10.1134/S0965542506100083