Category:Vanishing constraints

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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

  1. Achtziger, W., & Kanzow, C. (2008). Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications. Mathematical Programming Series A, 114, 69. Bib
  2. 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"

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