Category:Vanishing constraints

From Mintoc

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

$\begin{array}{llcl} \displaystyle \min_{y} & & & \Phi(y) \\[1.5ex] \mbox{s.t.} & 0 & \ge & g_i(y) h_i(y), \quad i \in \{1, \dots, m\}\\ & 0 & \le & \le h(y) \\ \end{array}$

with smooth functions $g, h: \R^{n_y} \mapsto \R^m$ is called MPVC. Note that every MPVC can be transformed into an MPEC ^[1]^[2]. Examples for vanishing constraints are engine speed constraints that are only active if the corresponding gear control is nonzero.

References

↑ Achtziger, W., & Kanzow, C. (2008). Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications. Mathematical Programming Series A, 114, 69. ^Bib
↑ Izmailov, A. F., & Solodov, M. V. (2009). Mathematical Programs with Vanishing Constraints: Optimality Conditions, Sensitivity, and a Relaxation Method. Journal of Optimization Theory and Applications, 142, 501. ^Bib

Pages in category "Vanishing constraints"

This category contains only the following page.

C

Car testdrive

[_note-achtziger2008] Achtziger, W., & Kanzow, C. (2008). Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications. Mathematical Programming Series A, 114, 69. ^Bib

[_note-izmailov2009] Izmailov, A. F., & Solodov, M. V. (2009). Mathematical Programs with Vanishing Constraints: Optimality Conditions, Sensitivity, and a Relaxation Method. Journal of Optimization Theory and Applications, 142, 501. ^Bib

[1]

[2]

Category:Vanishing constraints

From Mintoc

References

Pages in category "Vanishing constraints"

C

Views

Personal tools

Navigation

Search

Toolbox