Category:Boolean variables - Revision history

JonasSchulze: Text replacement - "" to ""

2016-01-23T10:10:59Z

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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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	<center><math>\delta_i: [0, t_f] \mapsto \{ \mathrm{true}, \mathrm{false} \}</math></center>		<center><math>\delta_i: [0, t_f] \mapsto \{ \mathrm{true}, \mathrm{false} \}</math></center>

	that indicate whether a model formulation <math>F_i[x,u,v]</math> is active at time <math>t</math>, 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 <~~bibref>~~Grossmann2002</~~bibref~~><~~bibref>~~Oldenburg2005</~~bibref~~><~~bibref>~~Oldenburg2008</~~bibref~~>.		that indicate whether a model formulation <math>F_i[x,u,v]</math> is active at time <math>t</math>, 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 <bib id="Grossmann2002" /><bib id="Oldenburg2005" /><bib id="Oldenburg2008" />.

	== References ==		== References ==

SebastianSager: Initial setup of IMA paper text

2010-11-20T11:36:47Z

Initial setup of IMA paper text

New page

Discrete switching events can also be expressed by means of Boolean variables and logical implications. E.g., by introducing logical functions
<center><math>\delta_i: [0, t_f] \mapsto \{ \mathrm{true}, \mathrm{false} \}</math></center>

that indicate whether a model formulation <math>F_i[x,u,v]</math> is active at time <math>t</math>, 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 <bibref>Grossmann2002</bibref><bibref>Oldenburg2005</bibref><bibref>Oldenburg2008</bibref>.

== References ==
<bibreferences/>

[[Category:Model characterization]]