Convex analysis in groups and semigroups: a sampler

• 成果类型: Article
• 署名作者: Borwein, Jonathan M.; Giladi, Ohad
• 署名单位: University of Newcastle
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1010-x
• 发表日期: 2018
• 页码: 11-53
• 关键词: continuity

摘要

We define convexity canonically in the setting of monoids. We show that many classical results from convex analysis hold for functions defined on such groups and semigroups, rather than only vector spaces. Some examples and counter-examples are also discussed.