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, [Baumrucker2009]Author: B.T. Baumrucker; L.T. Biegler
Journal: Journal of Process Control
Note: Special Section on Hybrid Systems: Modeling, Simulation and Optimization
Number: 8
Pages: 1248--1256
Title: MPEC strategies for optimization of a class of hybrid dynamic systems
Volume: 19
Year: 2009
. Note that all MPCCs can be reformulated as MPECs.

References

[Baumrucker2009]

B.T. Baumrucker; L.T. Biegler (2009): MPEC strategies for optimization of a class of hybrid dynamic systems. Journal of Process Control, 19, 1248--1256

This category currently contains no pages or media.