Category:Complementarity constraints

This category contains optimization problems with complementarity constraints (MPCCs), for generic variables / functions $y_{1}, y_{2}, y_{3}$ in the form of

$\begin{array}{llcl} \min_{y_{1}, y_{2}, y_{3}} & Φ (y_{1}, y_{2}, y_{3}) \\ s.t. & 0 & = & F (y_{1}, y_{2}, y_{3}), \\ 0 & \leq & C (y_{1}, y_{2}, y_{3}), \\ 0 & \leq & y_{1} ⊥ y_{2} \geq 0, \end{array}$

The complementarity operator $⊥$ implies the disjunctive behavior

y_{1, i} = 0 OR y_{2, i} = 0 \forall i = 1 \dots n_{y} .

MPCCs may arise from a reformulation of a bilevel optimization problem by writing the optimality conditions of the inner problem as variational constraints of the outer optimization problem, or from a special treatment of state-dependent switches, <bibref>Baumrucker2009</bibref>. Note that all MPCCs can be reformulated as MPECs.

References

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