论文标题
在优化理论中的定向渐近方法B部分：约束资格
On the directional asymptotic approach in optimization theory Part B: constraint qualifications
论文作者
论文摘要
在过去的几年中，渐近（或顺序）约束条件的资格，假定某些设定值映射的上半个映射上的上半座位，并提供了自然的渐近性平稳性条件的伴侣，在一方面是相对较小的，同时从另一方面具有固有的实践相关性，从而在另一个方面具有固有的实践相关性。基于最近的发展，本文中的理论丰富了渐近约束资格，用于通过合并定向数据，在集合值映射的反式图像上进行非常普遍的非平滑优化问题。我们将这些新的定向渐近规则条件与非平滑优化的标准约束资格进行了比较。此外，我们介绍了适用于设定值映射的伪正常和准正常的定向概念。结果表明，这些特性为定向渐近规则性的有效性提供了足够的条件。最后，引入了一种新型的代码样变异工具，该工具允许研究定向渐近规则的存在。对于几何约束，可以说明所有出现对象都可以根据初始问题数据计算。
During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be comparatively mild, on the one hand, while possessing inherent practical relevance from the viewpoint of numerical solution methods, on the other one. Based on recent developments, the theory in this paper enriches asymptotic constraint qualifications for very general nonsmooth optimization problems over inverse images of set-valued mappings by incorporating directional data. We compare these new directional asymptotic regularity conditions with standard constraint qualifications from nonsmooth optimization. Further, we introduce directional concepts of pseudo- and quasi-normality which apply to set-valued mappings. It is shown that these properties provide sufficient conditions for the validity of directional asymptotic regularity. Finally, a novel coderivative-like variational tool is introduced which allows to study the presence of directional asymptotic regularity. For geometric constraints, it is illustrated that all appearing objects can be calculated in terms of initial problem data.
