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Optimization theory in Banach spaces suffers from the lack of availableconstraint qualifications. Despite the fact that there exist only a very fewconstraint qualifications, they are, in addition, often violated even in simpleapplications. This is very much in contrast to finite-dimensional nonlinearprograms, where a large number of constraint qualifications is known. Sincethese constraint qualifications are usually defined using the set of activeinequality constraints, it is difficult to extend them to theinfinite-dimensional setting. One exception is a recently introduced sequentialconstraint qualification based on asymptotic KKT conditions. This paper showsthat this so-called asymptotic KKT regularity allows suitable extensions to theBanach space setting in order to obtain new constraint qualifications. Therelation of these new constraint qualifications to existing ones is discussedin detail. Their usefulness is also shown by several examples as well as analgorithmic application to the class of augmented Lagrangian methods.

New Constraint Qualifications for Optimization Problems in Banach Spaces based on Asymptotic KKT Conditions