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 y_1, y_2 the following general form:

 \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),

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.

Complementarity constraints and vanishing constraints are special cases.

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