TY - GEN A1 - Börgens, Eike A1 - Kanzow, Christian A1 - Mehlitz, Patrick A1 - Wachsmuth, Gerd T1 - New Constraint Qualifications for Optimization Problems in Banach Spaces Based on Asymptotic KKT Conditions T2 - SIAM Journal on Optimization N2 - Optimization theory in Banach spaces suffers from a lack of available constraint qualifications. There exist very few constraint qualifications, and these are often violated even in simple applications. This is very much in contrast to finite-dimensional nonlinear programs, where a large number of constraint qualifications is known. Since these constraint qualifications are usually defined using the set of active inequality constraints, it is difficult to extend them to the infinite-dimensional setting. One exception is a recently introduced sequential constraint qualification based on asymptotic KKT conditions. This paper shows that this so-called asymptotic KKT regularity allows suitable extensions to the Banach space setting in order to obtain new constraint qualifications. The relation of these new constraint qualifications to existing ones is discussed in detail. Their usefulness is also shown by several examples as well as an algorithmic application to the class of augmented Lagrangian methods. KW - asymptotic KKT conditions KW - asymptotic KKT regularity KW - constraint qualifications KW - optimization in Banach spaces KW - augmented Lagrangian method Y1 - 2020 U6 - https://doi.org/10.1137/19M1306804 SN - 1095-7189 SN - 1052-6234 VL - 30 IS - 4 SP - 2956 EP - 2982 ER -