View source for Category:Equilibrium constraints

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]]