Category:Vanishing constraints: Difference between revisions

Revision as of 17:54, 20 January 2016

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

Pages in category "Vanishing constraints"

This category contains only the following page.

C

Car testdrive

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-with smooth functions <math>g, h: \R^{n_y} \mapsto \R^m</math> is called MPVC. Note that every MPVC can be transformed into an [[:Category:Equilibrium constraints | MPEC]] <bibref>Achtziger2008</bibref><bibref>Izmailov2009</bibref>. Examples for vanishing constraints are engine speed constraints that are only active if the corresponding gear control is nonzero.
+with smooth functions <math>g, h: \R^{n_y} \mapsto \R^m</math> is called MPVC. Note that every MPVC can be transformed into an [[:Category:Equilibrium constraints | MPEC]] <bib id="Achtziger2008" /><bib id="Izmailov2009" />. Examples for vanishing constraints are engine speed constraints that are only active if the corresponding gear control is nonzero.
 == References ==