Convex analysis in groups and semigroups: a sampler

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.

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Veröffentlicht in:	Mathematical programming 2018-03, Vol.168 (1-2), p.11-53
Hauptverfasser:	Borwein, Jonathan M., Giladi, Ohad
Format:	Artikel
Sprache:	eng
Schlagworte:	Calculus of Variations and Optimal Control Optimization Combinatorics Convex analysis Convexity Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Monoids Numerical Analysis Theoretical Vector spaces
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Beschreibung
Zusammenfassung:	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.
ISSN:	0025-5610 1436-4646
DOI:	10.1007/s10107-016-1010-x