Generalized Derivatives of Lexicographic Linear Programs

Jose Alberto Gomez (), Kai Höffner (), Kamil A. Khan () and Paul I. Barton ()
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Jose Alberto Gomez: Massachusetts Institute of Technology
Kai Höffner: Massachusetts Institute of Technology
Kamil A. Khan: Massachusetts Institute of Technology
Paul I. Barton: Massachusetts Institute of Technology

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 2, No 9, 477-501

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.

Keywords: Linear programming; Lexicographic linear programming; Lexicographic optimization; Nonsmooth analysis; Generalized derivatives; Lexicographic differentiation; Nonsmooth equation solving; 49J52; 90C05; 90C29; 90C31 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-018-1309-2

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