DagSemProc.09261.31.pdf
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The Transport PDE and Mixed-Integer Linear Programming
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Dagstuhl Seminar Proceedings, Volume 9261
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication date: 2009-10-02
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Armin Fügenschuh, Björn Geißler, Alexander Martin, and Antonio Morsi. The Transport PDE and Mixed-Integer Linear Programming. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DagSemProc.09261.31
https://doi.org/10.4230/DagSemProc.09261.31
Abstract
Discrete, nonlinear and PDE constrained optimization are mostly considered as
different fields of mathematical research. Nevertheless many real-life problems
are most naturally modeled as PDE constrained mixed integer nonlinear programs.
For example, nonlinear network flow problems where the flow dynamics are
governed by a transport equation are of this type. We present four different
applications together with the derivation of the associated transport equations
and we show how to model these problems in terms of mixed integer linear
constraints.
Keywords
- Transport Equation
- Partial Differential Equation
- Mixed-Integer Linear Programming
- Modeling
- Nonlinear Constraints
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