Category:Boolean variables
From Mintoc
Discrete switching events can also be expressed by means of Boolean variables and logical implications. E.g., by introducing logical functions
![\delta_i: [0, t_f] \mapsto \{ \mathrm{true}, \mathrm{false} \}](/images/math/1/2/f/12f0eb048533d6e0735023f25291eb9a.png)
that indicate whether a model formulation Fi[x,u,v] is active at time t, both state-dependent switches and outer convexification formulations may be written as disjunctive programs, i.e., optimization problems involving Boolean variables and logical conditions. Using disjunctive programs can be seen as a more natural way of modeling discrete events and has the main advantage of resulting in tighter relaxations of the discrete dicisions, when compared to integer programming techniques. More details can be found, e.g., in [1][2][3].
References
- ↑ Grossmann, I. E. (2002). Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques. Optimization and Engineering, 3, 227. Bib
- ↑ Oldenburg, J. (2005). Logic–based modeling and optimization of discrete–continuous dynamic systems (Vol. 830). Düsseldorf: VDI Verlag. Bib
- ↑ Oldenburg, J., & Marquardt, W. (2008). Disjunctive modeling for optimal control of hybrid systems. Computers and Chemical Engineering, 32(10), 2346. Bib
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