Category:Equilibrium constraints - Revision history

SebastianSager at 12:15, 20 November 2010

2010-11-20T12:15:39Z

← Older revision		Revision as of 12:15, 20 November 2010
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	where <math>Y(y_1)</math> is the feasible region for the variational inequality and given function <math>\phi(\cdot)</math>. Variational inequalities arise in many domains and are generally referred to as equilibrium constraints. The variables <math>y_1</math> and <math>y_2</math> may be controls or states.		where <math>Y(y_1)</math> is the feasible region for the variational inequality and given function <math>\phi(\cdot)</math>. Variational inequalities arise in many domains and are generally referred to as equilibrium constraints. The variables <math>y_1</math> and <math>y_2</math> may be controls or states.

	[[:Category:Complementarity constraints \| Complementarity constraints]] are a special ~~case~~.		[[:Category:Complementarity constraints \| Complementarity constraints]] and [[:Category:Vanishing constraints \| vanishing constraints]] are special cases.

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

SebastianSager: Correction

2010-11-20T12:05:35Z

Correction

← Older revision		Revision as of 12:05, 20 November 2010
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	<math>		<math>
	\begin{array}{llcl}		\begin{array}{llcl}
	\displaystyle \min_{y_1, y_2, y_3} & \Phi(y_1, y_2, y_3) \\[1.5ex]		\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), \\		\mbox{s.t.} & 0 & = & F ( y_1, y_2, y_3), \\
	& 0 & \le & C ( y_1, y_2, y_3), \\		& 0 & \le & C ( y_1, y_2, y_3), \\
	& 0 & \le & y_1 \~~perp~~ y_2 \~~ge 0~~,		& 0 & \le & (\mu - y_2)^T \; \phi( y_1, y_2), \; y_2 \in Y(y_1), \; \forall \mu \in Y(y_1),
	\end{array}		\end{array}
	</math>		</math>
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	where <math>Y(y_1)</math> is the feasible region for the variational inequality and given function <math>\phi(\cdot)</math>. Variational inequalities arise in many domains and are generally referred to as equilibrium constraints. The variables <math>y_1</math> and <math>y_2</math> may be controls or states.		where <math>Y(y_1)</math> is the feasible region for the variational inequality and given function <math>\phi(\cdot)</math>. Variational inequalities arise in many domains and are generally referred to as equilibrium constraints. The variables <math>y_1</math> and <math>y_2</math> may be controls or states.

			[[:Category:Complementarity constraints \| Complementarity constraints]] are a special case.

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

SebastianSager: Initial setup of IMA paper text

2010-11-20T11:58:10Z

Initial setup of IMA paper text

New page

This category contains mathematical programs with equilibrium constraints (MPECs). An MPEC is an optimization problem constrained by a variational inequality, which takes for generic variables / functions <math>y_1, y_2</math> the following general form:

<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>

where <math>Y(y_1)</math> is the feasible region for the variational inequality and given function <math>\phi(\cdot)</math>. Variational inequalities arise in many domains and are generally referred to as equilibrium constraints. The variables <math>y_1</math> and <math>y_2</math> may be controls or states.

[[Category:Objective characterization]]