Add definition of the prox to the docs, use the same date format as i…

…n Manopt.jl
JuliaManifolds · Dec 6, 2023 · c372581 · c372581
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diff --git a/Changelog.md b/Changelog.md
@@ -5,7 +5,7 @@ All notable changes to this Julia package will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
-## [0.3.9] – 4. December 2023
+## [0.3.9] - December 4, 2023
 
 ### Added
 

diff --git a/docs/src/library.md b/docs/src/library.md
@@ -54,6 +54,17 @@ Order = [:type, :function, :constant]
 
 ## Proximal Maps
 
+Given a function ``f\colon \mathcal M \to \mathbb R``, its proximal map is defined
+for some ``λ>0`` as [Bacak:2014](@cite)
+
+```math
+\operatorname*{prox}_{λf}(p) := \operatorname{arg\,min}_{q\in\mathcal M} d_{\mathcal M}(p,q) + f(q).
+```
+
+Another name for the proximal map is _resolvent
+Intuitively this means to minimize the function ``f`` while at the same timme “staying close”
+to the argument ``p``.
+
 ```@autodocs
 Modules = [ManifoldDiff]
 Pages = ["proximal_maps.jl"]

diff --git a/docs/src/references.bib b/docs/src/references.bib
@@ -6,6 +6,18 @@ @book{AbsilMahonySepulchre:2008
     TITLE     = {Optimization Algorithms on Matrix Manifolds},
     YEAR      = {2008},
 }
+
+@article{Bacak:2014,
+    AUTHOR  = {Bačák, M.},
+    DOI     = {10.1137/140953393},
+    JOURNAL = {SIAM Journal on Optimization},
+    NUMBER  = {3},
+    PAGES   = {1542--1566},
+    TITLE   = {Computing medians and means in Hadamard spaces},
+    VOLUME  = {24},
+    YEAR    = {2014}
+}
+
 @book{Boumal:2023,
     TITLE     = {An Introduction to Optimization on Smooth Manifolds},
     AUTHOR    = {Boumal, Nicolas},