Lexicographic Duality in Linear Optimization

  • I. I. Eremin
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 374)


By lexicographic maximization of the system of functions {fi(x)} 0 k on a set M corresponding to permutation p = (i 0,...,i k) we mean the problem: Find 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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  1. 1.
    Eremin I.I. On the problems of successive programming // Sib. matem. jurn. 1973. T.14, No.1. P.53–63. (in Russian).Google Scholar
  2. 2.
    Eremin I.I. Penalty function method in convex programming // Dokl. AN SSSR. 1967. T.173, No.4. P.748–751. (in Russian).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • I. I. Eremin
    • 1
  1. 1.Institute of Mathematics and MechanicsUral Branch of the USSR Academy of SciencesSverdlovskUSSR

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