Difference between revisions of "Category:Equilibrium constraints"
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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 \ | + | & 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]] | ||
Revision as of 13:05, 20 November 2010
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 
the following general form:
![\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 & (\mu - y_2)^T \; \phi( y_1, y_2), \; y_2 \in Y(y_1), \; \forall \mu \in Y(y_1),
\end{array}](https://mintoc.de/images/math/f/4/d/f4d20f04f516a6ae8307a4f50497aed6.png)
where 
is the feasible region for the variational inequality and given function 
. Variational inequalities arise in many domains and are generally referred to as equilibrium constraints. The variables 
and 
may be controls or states.
Complementarity constraints are a special case.
This category currently contains no pages or media.
