Necessary conditions for non-intersection of collections of sets. (2nd January 2022)

• Record Type: Journal Article
• Authors: Bui, Hoa T.; Kruger, Alexander Y.
• Is Part Of: Optimization. Volume 71:Number 1(2022)
• Page Start: 165
• Page End: 196
• Publication Date: 2022-01-02
• Subjects: Extremal principle -- transversality -- regularity -- separation -- alternating projections; 49J52 -- 49J53 -- 49K40 -- 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1901899
• Languages: English
• ISSNs: 0233-1934

Abstract

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.