Category:Complementarity constraints - Revision history

JonasSchulze: Text replacement - "" to ""

2016-01-23T10:11:00Z

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

← Older revision		Revision as of 10:11, 23 January 2016
Line 22:		Line 22:

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

	[[Category:Objective characterization]]		[[Category:Objective characterization]]

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

2016-01-20T17:54:23Z

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

← Older revision		Revision as of 17:54, 20 January 2016
Line 18:		Line 18:
	</math></center>		</math></center>

	MPCCs may arise from a reformulation of a bilevel optimization problem by writing the optimality conditions of the inner problem as variational constraints of the outer optimization problem, or from a special treatment of state-dependent switches, <~~bibref>~~Baumrucker2009</~~bibref~~>. Note that all MPCCs can be reformulated as [[:Category:Equilibrium constraints \| MPECs]].		MPCCs may arise from a reformulation of a bilevel optimization problem by writing the optimality conditions of the inner problem as variational constraints of the outer optimization problem, or from a special treatment of state-dependent switches, <bib id="Baumrucker2009" />. Note that all MPCCs can be reformulated as [[:Category:Equilibrium constraints \| MPECs]].

SebastianSager: Initial setup of IMA paper text

2010-11-20T12:02:40Z

Initial setup of IMA paper text

New page

This category contains optimization problems with complementarity constraints (MPCCs), for generic variables / functions <math>y_1, y_2, y_3</math> in the form of

<center>
<math>
\begin{array}{llcl}
\displaystyle \min_{y_1, y_2, y_3} & & & \Phi(y_1, y_2, y_3) \\[1.5ex]
\mbox{s.t.} & 0 & = & F ( y_1, y_2, y_3), \\
& 0 & \le & C ( y_1, y_2, y_3), \\
& 0 & \le & y_1 \perp y_2 \ge 0,
\end{array}
</math>
</center>

The complementarity operator <math>\perp</math> implies the disjunctive behavior

<center><math>
y_{1,i} = 0 \quad{\mbox{ OR } }\quad y_{2,i} = 0 \quad \quad \forall \; i = 1 \dots n_y.
</math></center>

MPCCs may arise from a reformulation of a bilevel optimization problem by writing the optimality conditions of the inner problem as variational constraints of the outer optimization problem, or from a special treatment of state-dependent switches, <bibref>Baumrucker2009</bibref>. Note that all MPCCs can be reformulated as [[:Category:Equilibrium constraints | MPECs]].

== References ==
<bibreferences/>

[[Category:Objective characterization]]