About [q]-regularity properties of collections of sets

作者：Kruger Alexander Y^*; Thao Nguyen H

来源：Journal of Mathematical Analysis and Applications, 2014, 416(2): 471-496.

DOI：10.1016/j.jmaa.2014.02.028

• Metric regularity
• Uniform regularity
• Normal cone
• Subdifferential

We examine three primal space local Holder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent metric characterizations of the three mentioned regularity properties as well as a sufficient condition of [q]-subregularity in terms of Frechet normals are established. The relationships between [q]-regularity properties of collections of sets and the corresponding regularity properties of set-valued mappings are discussed.

• 出版日期2014-8-15