- Title
- Convex analysis in groups and semigroups: a sampler
- Creator
- Borwein, Jonathan M.; Giladi, Ohad
- Relation
- ARC
- Relation
- Mathematical Programming Vol. 168, Issue 1-2, p. 11-53
- Publisher Link
- http://dx.doi.org/10.1007/s10107-016-1010-x
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2018
- Description
- 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.
- Subject
- convexity; semimodule; monoid; Hahn-Banach theory; Fenchel duality; Vector-valued convexity
- Identifier
- http://hdl.handle.net/1959.13/1409244
- Identifier
- uon:35977
- Identifier
- ISSN:0025-5610
- Rights
- This is a post-peer-review, pre-copyedit version of an article published in Mathematical Programming. The final authenticated version is available online at: https://doi.org/10.1007/s10107-016-1010-x.
- Language
- eng
- Full Text
- Reviewed
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