Variational principles on topological spaces. (1st September 2020)

• Record Type: Journal Article
• Authors: Zheng, Xi Yin; Zhu, Jiangxing
• Is Part Of: Optimization. Volume 69:Number 9(2020)
• Page Start: 1881
• Page End: 1893
• Publication Date: 2020-09-01
• Subjects: Topological space -- Cantor-compatibility -- strong minimizer -- variational principle; 49K40 -- 90C26; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1671384
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : To the best of our knowledge, all the existing variational principles were established in the framework of a complete metric space or a Banach space. In this paper, we consider variational principles in topological spaces. We adopt gauge-type functions on a topological space X and introduce the notion of the Cantor compatibility for X and gauge-type functions on X . In terms of the Cantor-compatibility, we provide strong variational principles on a topological space, which further extend both the Ekeland variational principle and the Borwein-Preiss smooth variational principle.