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 $y_1, y_2$ the following general form:

$\begin{array}{llcl} \displaystyle \min_{y_1, y_2, y_3} & & & \Phi(y_1, y_2, y_3) \\[1.5ex] \mbox{s.t.} & 0 & = & F ( y_1, y_2, y_3), \\ & 0 & \le & C ( y_1, y_2, y_3), \\ & 0 & \le & (\mu - y_2)^T \; \phi( y_1, y_2), \; y_2 \in Y(y_1), \; \forall \mu \in Y(y_1), \end{array}$

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