Category:Outer convexification - Revision history

JonasSchulze: Text replacement - "" to ""

2016-01-23T10:10:58Z

Text replacement - "<bibreferences/>" to "<biblist />"

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	== References ==		== References ==
	<~~bibreferences~~/>		<biblist />

	[[Category:Model characterization]]		[[Category:Model characterization]]

JonasSchulze: Text replacement - "\(.*)\<\/bibref\>" to ""

2016-01-20T17:54:23Z

Text replacement - "\<bibref\>(.*)\<\/bibref\>" to "<bib id="$1" />"

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

	The general equation		The general equation
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	</center>		</center>

	there is a bijection between every feasible integer function <math>v(\cdot) \in \Omega</math> and an appropriately chosen binary function <math>\omega(\cdot) \in \{0,1\}^{n_{\omega}}</math>, compare <~~bibref>~~Sager2009</~~bibref~~>. The relaxation of <math>\omega(t) \in \{0,1\}^{n_{\omega}}</math> is given by <math>\omega(t) \in [0,1]^{n_{\omega}}</math>. We will refer to the two constraints as ''outer convexification'' <~~bibref>~~Sager2005</~~bibref~~> of the original model.		there is a bijection between every feasible integer function <math>v(\cdot) \in \Omega</math> and an appropriately chosen binary function <math>\omega(\cdot) \in \{0,1\}^{n_{\omega}}</math>, compare <bib id="Sager2009" />. The relaxation of <math>\omega(t) \in \{0,1\}^{n_{\omega}}</math> is given by <math>\omega(t) \in [0,1]^{n_{\omega}}</math>. We will refer to the two constraints as ''outer convexification'' <bib id="Sager2005" /> of the original model.

	== References ==		== References ==

SebastianSager at 11:29, 20 November 2010

2010-11-20T11:29:30Z

← Older revision		Revision as of 11:29, 20 November 2010
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	</center>		</center>

	there is a bijection between every feasible integer function <math>v(\cdot) \in \Omega</math> and an appropriately chosen binary function <math>\omega(\cdot) \in \{0,1\}^{n_{\omega}}</math>, compare <bibref>Sager2009</bibref>. The relaxation of <math>\omega(t) \in \{0,1\}^{n_{\omega}}</math> is given by <math>\omega(t) \in [0,1]^{n_{\omega}}</math>. We will refer to the two constraints as ''outer convexification'' of the original model.		there is a bijection between every feasible integer function <math>v(\cdot) \in \Omega</math> and an appropriately chosen binary function <math>\omega(\cdot) \in \{0,1\}^{n_{\omega}}</math>, compare <bibref>Sager2009</bibref>. The relaxation of <math>\omega(t) \in \{0,1\}^{n_{\omega}}</math> is given by <math>\omega(t) \in [0,1]^{n_{\omega}}</math>. We will refer to the two constraints as ''outer convexification'' <bibref>Sager2005</bibref> of the original model.


	== References ==		== References ==

SebastianSager at 11:28, 20 November 2010

2010-11-20T11:28:32Z

← Older revision		Revision as of 11:28, 20 November 2010
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	</center>		</center>

	there is a bijection between every feasible integer function <math>v(\cdot) \in \Omega</math> and an appropriately chosen binary function <math>\omega(\cdot) \in \{0,1\}^{n_{\omega}}</math>, compare <bibref>Sager2009</bibref>. The relaxation of <math>\omega(t) \in \{0,1\}^{n_{\omega}}</math> is given by <math>\omega(t) \in [0,1]^{n_{\omega}}</math>. We will refer to the two constraints as ~~{\it~~ outer convexification} of the original model.		there is a bijection between every feasible integer function <math>v(\cdot) \in \Omega</math> and an appropriately chosen binary function <math>\omega(\cdot) \in \{0,1\}^{n_{\omega}}</math>, compare <bibref>Sager2009</bibref>. The relaxation of <math>\omega(t) \in \{0,1\}^{n_{\omega}}</math> is given by <math>\omega(t) \in [0,1]^{n_{\omega}}</math>. We will refer to the two constraints as ''outer convexification'' of the original model.

SebastianSager: Initial setup of IMA paper text

2010-11-20T11:28:00Z

Initial setup of IMA paper text

New page

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

The general equation
<center>
<math>
0 = F[x,u,v(t)]
</math>
</center>
can then be written as

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

If we impose the special ordered set type one condition

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

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

== References ==
<bibreferences/>

[[Category:Model characterization]]