Efficient solution of ordinary differential equations with a parametric lexicographic linear program embedded
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Author(s)
Höffner, Kai
Barton, Paul I.
Harwood, Stuart Maxwell
Hoeffner, Kai
Date Issued
July 2015
Journal
Numerische Mathematik
Publisher
Springer Berlin Heidelberg
Citation
Harwood, Stuart M., Kai Höffner, and Paul I. Barton. “Efficient Solution of Ordinary Differential Equations with a Parametric Lexicographic Linear Program Embedded.” Numerische Mathematik 133, no. 4 (July 29, 2015): 623–653.
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Author's final manuscript
Abstract
This work analyzes the initial value problem in ordinary differential equations with a parametric lexicographic linear program (LP) embedded. The LP is said to be embedded since the dynamics depend on the solution of the LP, which is in turn parameterized by the dynamic states. This problem formulation finds application in dynamic flux balance analysis, which serves as a modeling framework for industrial fermentation reactions. It is shown that the problem formulation can be intractable numerically, which arises from the fact that the LP induces an effective domain that may not be open. A numerical method is developed which reformulates the system so that it is defined on an open set. The result is a system of semi-explicit index-one differential algebraic equations, which can be solved with efficient and accurate methods. It is shown that this method addresses many of the issues stemming from the original problem’s intractability. The application of the method to examples of industrial fermentation processes demonstrates its effectiveness and efficiency.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Massachusetts Institute of Technology. Process Systems Engineering Laboratory
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DOI of Published Version
https://doi.org/10.1007/s00211-015-0760-3
