Generalized Derivatives of Lexicographic Linear Programs
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10957_2018_1309_ReferencePDF.pdf
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Author(s)
Gomez, Jose A
Höffner, Kai
Khan, Kamil A
Barton, Paul I
Date Issued
May 23, 2018
Publisher
Springer US
Version
Author's final manuscript
Abstract
Abstract
Lexicographic linear programs are fixed-priority multiobjective linear programs that are a useful model of biological systems using flux balance analysis and for goal-programming problems. The objective function values of a lexicographic linear program as a function of its right-hand side are nonsmooth. This work derives generalized derivative information for lexicographic linear programs using lexicographic directional derivatives to obtain elements of the Bouligand subdifferential (limiting Jacobian). It is shown that elements of the limiting Jacobian can be obtained by solving related linear programs. A nonsmooth equation-solving problem is solved to illustrate the benefits of using elements of the limiting Jacobian of lexicographic linear programs.
MIT Department
Massachusetts Institute of Technology. Process Systems Engineering Laboratory
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10957-018-1309-2
