Perspective Functions: Properties, Constructions, and Examples
By Patrick L. Combettes. Set-Valued and Variational Analysis, 2016
74 citations recorded by the source corpus.
Many functions encountered in applied mathematics and in statistical data analysis can be expressed in terms of perspective functions. One of the earliest examples is the Fisher information, which appeared in statistics in the 1920s. We analyze various algebraic and convex-analytical properties of perspective functions and provide general schemes to construct lower semicontinuous convex functions from them. Several new examples are presented and existing instances are featured as special cases.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/aa1792f62aa8460757458280e0c5212cf8470202
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Christian L. Muller
- Patrick L. Combettes
- Laurent Condat
- Ernö Robert Csetnek
- Radu Ioan Bot
- Bang Công Vu
- Jong Chul Ye
- Marcelo Pereyra
In Computational Theory and Mathematics
- Christian L. Muller
- Patrick L. Combettes
- Jean-Christophe Pesquet
- Laurent Condat
- Luis M. Briceño-Arias
- Heinz H. Bauschke
- Bang Công Vu
- Simeon Reich
In Numerical Analysis
- Christian L. Muller
- Patrick L. Combettes
- Simeon Reich
- Heinz H. Bauschke
- Laurent Condat
- Bang Công Vu
- Gilbert Crombez
- Fenghui Wang
Citations in the corpus
- Perspective Functions: Proximal Calculus and Applications in High-Dimensional Statistics (2016, background): “s a cone. Then C= D, σD= ιK, and (2.16) yields Id −PD= PK. Altogether, (2.18) reduces to (2.19). 2.3 Perspective functions We review here some essential properties of perspective functions. Lemma 2.3 [7] Let ϕ∈ Γ0(G). Then the following hold: (i) ϕe is a positively homogeneous function in Γ0(R⊕G). (”