First- and second-order optimality conditions for mathematical programs with vanishing constraints

Tim Hoheisel; Christian Kanzow

Applications of Mathematics (2007)

  • Volume: 52, Issue: 6, page 495-514
  • ISSN: 0862-7940

Abstract

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We consider a special class of optimization problems that we call Mathematical Programs with Vanishing Constraints, MPVC for short, which serves as a unified framework for several applications in structural and topology optimization. Since an MPVC most often violates stronger standard constraint qualification, first-order necessary optimality conditions, weaker than the standard KKT-conditions, were recently investigated in depth. This paper enlarges the set of optimality criteria by stating first-order sufficient and second-order necessary and sufficient optimality conditions for MPVCs.

How to cite

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Hoheisel, Tim, and Kanzow, Christian. "First- and second-order optimality conditions for mathematical programs with vanishing constraints." Applications of Mathematics 52.6 (2007): 495-514. <http://eudml.org/doc/33305>.

@article{Hoheisel2007,
abstract = {We consider a special class of optimization problems that we call Mathematical Programs with Vanishing Constraints, MPVC for short, which serves as a unified framework for several applications in structural and topology optimization. Since an MPVC most often violates stronger standard constraint qualification, first-order necessary optimality conditions, weaker than the standard KKT-conditions, were recently investigated in depth. This paper enlarges the set of optimality criteria by stating first-order sufficient and second-order necessary and sufficient optimality conditions for MPVCs.},
author = {Hoheisel, Tim, Kanzow, Christian},
journal = {Applications of Mathematics},
keywords = {mathematical programs with vanishing constraints; mathematical programs with equilibrium constraints; first-order optimality conditions; second-order optimality conditions; mathematical programs with vanishing constraints; mathematical programs with equilibrium constraints; first-order optimality conditions; second-order optimality conditions},
language = {eng},
number = {6},
pages = {495-514},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {First- and second-order optimality conditions for mathematical programs with vanishing constraints},
url = {http://eudml.org/doc/33305},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Hoheisel, Tim
AU - Kanzow, Christian
TI - First- and second-order optimality conditions for mathematical programs with vanishing constraints
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 6
SP - 495
EP - 514
AB - We consider a special class of optimization problems that we call Mathematical Programs with Vanishing Constraints, MPVC for short, which serves as a unified framework for several applications in structural and topology optimization. Since an MPVC most often violates stronger standard constraint qualification, first-order necessary optimality conditions, weaker than the standard KKT-conditions, were recently investigated in depth. This paper enlarges the set of optimality criteria by stating first-order sufficient and second-order necessary and sufficient optimality conditions for MPVCs.
LA - eng
KW - mathematical programs with vanishing constraints; mathematical programs with equilibrium constraints; first-order optimality conditions; second-order optimality conditions; mathematical programs with vanishing constraints; mathematical programs with equilibrium constraints; first-order optimality conditions; second-order optimality conditions
UR - http://eudml.org/doc/33305
ER -

References

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  11. 10.1287/moor.25.1.1.15213, Math. Oper. Res. 25 (2000), 1–22. (2000) MR1854317DOI10.1287/moor.25.1.1.15213
  12. 10.1137/S1052623499361233, SIAM J. Optim. 11 (2001), 918–936. (2001) Zbl1010.90086MR1855214DOI10.1137/S1052623499361233
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