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 …

A new class of optimization problems name'mathematical programs with vanishing
constraints (MPVCs)'is considered. MPVCs are on the one hand very challenging from a
theoretical viewpoint, since standard constraint qualifications such as LICQ, MFCQ, or ACQ
are most often violated, and hence, the Karush-Kuhn-Tucker conditions do not provide
necessary optimality conditions off-hand. Thus, new CQs and the corresponding optimality
conditions are investigated. On the other hand, MPVCs have important applications, eg, in …