We study mathematical programs with vanishing constraints (MPVCs) from a topological point of view. We introduce the new concept of a T-stationary point for MPVC. Under the Linear Independence Constraint Qualification we derive an equivariant Morse Lemma at nondegenerate T-stationary points. Then, two basic theorems from Morse Theory (deformation theorem and cell-attachment theorem) are proved. Outside the T-stationary point set, continuous deformation of lower level sets can be performed. As a consequence, the topological data (such as the number of connected components) then remain invariant. However, when passing a T-stationary level, the topology of the lower level set changes via the attachment of a q-dimensional cell. The dimension q equals the stationary T-index of the (nondegenerate) T-stationary point. The stationary T-index depends on both the restricted Hessian of the Lagrangian and the number of bi-active vanishing constraints. Further, we prove that all T-stationary points are generically nondegenerate. The latter property is shown to be stable under C 2-perturbations of the defining functions. Finally, some relations w ... mehr

Zugehörige Institution(en) am KIT |
Institut für Operations Research (IOR) |

Publikationstyp |
Zeitschriftenaufsatz |

Jahr |
2012 |

Sprache |
Englisch |

Identifikator |
ISSN: 0925-5001 KITopen ID: 1000027504 |

Erschienen in |
Journal of Global Optimization |

Band |
52 |

Heft |
3 |

Seiten |
591-605 |

KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page