Category:Vanishing constraints

This category contains mathematical programs with vanishing constraints (MPVCs). The problem

$\begin{array}{llcl} \min_{y} & Φ (y) \\ s.t. & 0 & \geq & g_{i} (y) h_{i} (y), i \in {1, \dots, m} \\ 0 & \leq & \leq h (y) \end{array}$

with smooth functions $g, h : ℝ^{n_{y}} \mapsto ℝ^{m}$ is called MPVC. Note that every MPVC can be transformed into an MPEC [Achtziger2008]Author: W. Achtziger; C. Kanzow
Journal: Mathematical Programming Series A
Pages: 69--99
Title: Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications
Volume: 114
Year: 2008
[Izmailov2009]Author: A.F. Izmailov; M.V. Solodov
Journal: Journal of Optimization Theory and Applications
Pages: 501--532
Title: Mathematical Programs with Vanishing Constraints: Optimality Conditions, Sensitivity, and a Relaxation Method
Volume: 142
Year: 2009
. Examples for vanishing constraints are engine speed constraints that are only active if the corresponding gear control is nonzero.

References

[Achtziger2008]	W. Achtziger; C. Kanzow (2008): Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications. Mathematical Programming Series A, 114, 69--99
[Izmailov2009]	A.F. Izmailov; M.V. Solodov (2009): Mathematical Programs with Vanishing Constraints: Optimality Conditions, Sensitivity, and a Relaxation Method. Journal of Optimization Theory and Applications, 142, 501--532

Pages in category "Vanishing constraints"

This category contains only the following page.

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