Lexicographic Duality in Linear Optimization

Abstract

By lexicographic maximization of the system of functions {f_i(x)} ^k₀ on a set M corresponding to permutation p = (i ₀,...,i _k) 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

$$y = \left\{ {\left[ {{y_0}, \ldots ,{y_k}} \right]\;\left| {\;{y_t} = {f_{{i_t}}}\left( x \right),x \in M,\;t = 0, \ldots ,k} \right.} \right\}$$

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