On comparison of approximate solutions in vector optimization problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 10, pp. 1790-1801
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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.
@article{ZVMMF_2006_46_10_a7,
author = {Ya. I. Rabinovich},
title = {On comparison of approximate solutions in vector optimization problems},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1790--1801},
publisher = {mathdoc},
volume = {46},
number = {10},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a7/}
}
TY - JOUR AU - Ya. I. Rabinovich TI - On comparison of approximate solutions in vector optimization problems JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2006 SP - 1790 EP - 1801 VL - 46 IS - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a7/ LA - ru ID - ZVMMF_2006_46_10_a7 ER -
%0 Journal Article %A Ya. I. Rabinovich %T On comparison of approximate solutions in vector optimization problems %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2006 %P 1790-1801 %V 46 %N 10 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_10_a7/ %G ru %F ZVMMF_2006_46_10_a7
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/