Category:Equilibrium constraints
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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 & y_1 \perp y_2 \ge 0,
\end{array}](https://mintoc.de/images/math/9/2/5/92564e636fe9b5b8773db4cb51dd844d.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.
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