SIAM Journal on Optimization, Volume 30, Issue 4, Page 2956-2982, January 2020.
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.

中文翻译：

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基于渐近KKT条件的Banach空间中最优化问题的新约束条件

SIAM优化杂志，第30卷，第4期，第2956-2982页，2020年1月。
Banach空间中的优化理论缺乏可用的约束条件。约束条件很少，即使在简单的应用程序中也经常被违反。这与已知大量约束条件的有限维非线性程序大不相同。由于这些约束条件通常是使用主动不等式约束集定义的，因此很难将它们扩展到无限维设置。一个例外是最近引入的基于渐近KKT条件的顺序约束限定。本文表明，这种所谓的渐近KKT正则性允许对Banach空间设置进行适当的扩展，以获得新的约束条件。详细讨论了这些新约束条件与现有约束条件的关系。几个示例还展示了它们的有用性，以及在扩展拉格朗日方法类中的算法应用。