Category:Outer convexification

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For time-dependent and space- independent integer controls often another formulation is beneficial, e.g., <bibref>Kirches2010</bibref>. For every element v^i of \Omega a binary control function \omega_i(\cdot) is introduced.

The general equation


0 = F[x,u,v(t)]

can then be written as


0 = \sum_{i=1}^{n_{\omega}} F[x,u,v^i] \; \omega_i (t),  \;\;\;\; t \in [0, t_f].

If we impose the special ordered set type one condition


\sum_{i=1}^{n_{\omega}} \omega_i (t) = 1,  \;\;\;\; t \in [0, t_f],

there is a bijection between every feasible integer function v(\cdot) \in \Omega and an appropriately chosen binary function \omega(\cdot) \in \{0,1\}^{n_{\omega}}, compare <bibref>Sager2009</bibref>. The relaxation of \omega(t) \in \{0,1\}^{n_{\omega}} is given by \omega(t) \in [0,1]^{n_{\omega}}. We will refer to the two constraints as outer convexification <bibref>Sager2005</bibref> of the original model.

References

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Pages in category "Outer convexification"

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