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Published in:
1992 | OriginalPaper | Chapter
Lexicographic Duality in Linear Optimization
Author : I. I. Eremin
Published in: Simulation and Optimization
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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By lexicographic maximization of the system of functions {fi(x)}0k on a set M corresponding to permutation p = (i0,...,ik) we mean the problem: Find x̃∈M such that vector $$\left[ {{f_{{i_0}}}\left( {\tilde x} \right), \ldots ,{f_{{i_k}}}\left( {\tilde x} \right)} \right]$$ is a p-lexicographic maximum on the set $$y = \left\{ {\left[ {{y_0}, \ldots ,{y_k}} \right]\;\left| {\;{y_t} = {f_{{i_t}}}\left( x \right),x \in M,\;t = 0, \ldots ,k} \right.} \right\}$$.