The Transport PDE and Mixed-Integer Linear Programming

Discrete, nonlinear and PDE constrained optimization are mostly considered as dierent elds of mathematical research. Neverthe- less many real-life problems are most naturally modeled as PDE con- strained mixed integer nonlinear programs. For example, nonlinear net- work ow problems where the ow dynamics are governed by a transport equation are of this type. We present four dierent 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.

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