Category:Equilibrium constraints: Difference between revisions
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<math> | <math> | ||
\begin{array}{llcl} | \begin{array}{llcl} | ||
\displaystyle \min_{y_1, y_2, y_3} & \Phi(y_1, y_2, y_3) \\[1.5ex] | \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), \\ | \mbox{s.t.} & 0 & = & F ( y_1, y_2, y_3), \\ | ||
& 0 & \le & C ( y_1, y_2, y_3), \\ | & 0 & \le & C ( y_1, y_2, y_3), \\ | ||
& 0 & \le & y_1 \ | & 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} | \end{array} | ||
</math> | </math> | ||
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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. | 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]] and [[:Category:Vanishing constraints | vanishing constraints]] are special cases. | |||
[[Category:Objective characterization]] | [[Category:Objective characterization]] | ||
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 the following general form:
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.
Complementarity constraints and vanishing constraints are special cases.
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