Category:Equilibrium constraints: Difference between revisions

Latest revision as of 12:15, 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 $y_{1}, y_{2}$ the following general form:

$\begin{array}{llcl} \min_{y_{1}, y_{2}, y_{3}} & Φ (y_{1}, y_{2}, y_{3}) \\ s.t. & 0 & = & F (y_{1}, y_{2}, y_{3}), \\ 0 & \leq & C (y_{1}, y_{2}, y_{3}), \\ 0 & \leq & (μ - y_{2})^{T} ϕ (y_{1}, y_{2}), y_{2} \in Y (y_{1}), \forall μ \in Y (y_{1}), \end{array}$

where $Y (y_{1})$ is the feasible region for the variational inequality and given function $ϕ (\cdot)$ . 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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 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:Complementarity constraints | Complementarity constraints]] and [[:Category:Vanishing constraints | vanishing constraints]] are special cases.
 [[Category:Objective characterization]]