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arXiv · 1909.08995

Necessary Conditions for Non-Intersection of Collections of Sets

Hoa T. Bui·Alexander Y. Kruger
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Abstract

This paper continues studies of non-intersection properties of finite collections of sets initiated 40 years ago by the extremal principle. We study elementary non-intersection properties of collections of sets, making the core of the conventional definitions of extremality and stationarity. In the setting of general Banach/Asplund spaces, we establish new primal (slope) and dual (generalized separation) necessary conditions for these non-intersection properties. The results are applied to convergence analysis of alternating projections.

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Hoa T. Bui, Alexander Y. Kruger. 2019-09-18. Necessary Conditions for Non-Intersection of Collections of Sets. https://doi.org/10.1080/02331934.2021.1901899

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