Add technical details to the ARC solver.

JuliaManifolds · Nov 17, 2023 · a7edf1e · a7edf1e
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diff --git a/docs/.vale.ini b/docs/.vale.ini
@@ -1,9 +1,12 @@
 StylesPath = styles
-MinAlertLevel = error
+MinAlertLevel = warning
 Vocab = Manopt
 
 Packages = Google
 
+[formats]
+qmd = md
+
 [*.md]
 BasedOnStyles = Vale, Google
 TokenIgnores =          \

diff --git a/docs/src/notation.md b/docs/src/notation.md
@@ -1,8 +1,7 @@
 # Notation
 
-In this package, we follow the notation introduced in [Manifolds.jl Notation](https://juliamanifolds.github.io/Manifolds.jl/latest/misc/notation.html)
-
-with the following additional notation
+In this package,the notation introduced in [Manifolds.jl Notation](https://juliamanifolds.github.io/Manifolds.jl/latest/misc/notation.html) is used
+with the following additional parts.
 
 | Symbol | Description | Also used | Comment |
 |:--:|:--------------- |:--:|:-- |

diff --git a/docs/src/plans/index.md b/docs/src/plans/index.md
@@ -9,7 +9,7 @@ information is required about both the optimisation task or “problem” at han
 This together is called a __plan__ in `Manopt.jl` and it consists of two data structures:
 
 * The [Manopt Problem](@ref ProblemSection) describes all _static_ data of a task, most prominently the manifold and the objective.
-* The [Solver State](@ref SolverStateSection) describes all _varying_ data and parameters for the solver that is used. This also means that each solver has its own data structure for the state.
+* The [Solver State](@refsec:solver-state) describes all _varying_ data and parameters for the solver that is used. This also means that each solver has its own data structure for the state.
 
 By splitting these two parts, one problem can be define an then be solved  using different solvers.
 

diff --git a/docs/src/plans/state.md b/docs/src/plans/state.md
@@ -1,4 +1,4 @@
-# [The solver state](@id SolverStateSection)
+# [The solver state](@id sec-solver-state)
 
 ```@meta
 CurrentModule = Manopt

diff --git a/docs/src/solvers/adaptive-regularization-with-cubics.md b/docs/src/solvers/adaptive-regularization-with-cubics.md
@@ -54,6 +54,18 @@ StopWhenAllLanczosVectorsUsed
 StopWhenFirstOrderProgress
 ```
 
+## [Technical Details](@id sec-arc-technical-details)
+
+The [`adaptive_regularization_with_cubics`](@ref) requires the following functions
+of a manifolds to be available
+
+* A [retract!](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/retractions/)ion; it is recommended to set the [`default_retraction_method`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/retractions/#ManifoldsBase.default_retraction_method-Tuple{AbstractManifold}) to a favourite retraction. If this default is set, a `retraction_method=` does not have to be specified.
+* if you do not provide an initial regularization parameter `σ`, a [`manifold_dimension`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/functions/#ManifoldsBase.manifold_dimension-Tuple{AbstractManifold}) is required.
+* By default the tangent vector storing the gradient is initialized calling [`zero_vector`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/functions/#ManifoldsBase.zero_vector-Tuple{AbstractManifold,%20Any})`(M,p)`.
+* [`inner`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/functions/#ManifoldsBase.inner-Tuple{AbstractManifold,%20Any,%20Any,%20Any})`(M, p, X, Y)` is used within the algorithm step
+
+Furthermore, within the Lanczos subsolver, generating a random vector (at `p`) using [`rand!`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/functions/#Base.rand-Tuple{AbstractManifold})`(M, X; vector_at=p)` in place of `X` is required
+
 ## Literature
 
 ```@bibliography

diff --git a/docs/src/solvers/gradient_descent.md b/docs/src/solvers/gradient_descent.md
@@ -43,9 +43,9 @@ RecordGradientNorm
 RecordStepsize
 ```
 
-## [Technical Details](@id GradientDescent-Technical-Details)
+## [Technical Details](@id sec-gradient-descent-technical-details)
 
-The [`gradient_descent`](@ref) solver requires the following functions of your manifold to be available
+The [`gradient_descent`](@ref) solver requires the following functions of a manifold to be available
 
 * A [retract!](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/retractions/)ion; it is recommended to set the [`default_retraction_method`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/retractions/#ManifoldsBase.default_retraction_method-Tuple{AbstractManifold}) to a favourite retraction,
 for this case it does not have to be specified.

diff --git a/docs/src/solvers/index.md b/docs/src/solvers/index.md
@@ -31,7 +31,7 @@ The following algorithms are currently available
 [Primal-dual Riemannian semismooth Newton Algorithm](@ref PDRSSNSolver) | [`primal_dual_semismooth_Newton`](@ref),  [`PrimalDualSemismoothNewtonState`](@ref) (using [`TwoManifoldProblem`](@ref)) | ``f=F+G(Λ\cdot)``, ``\operatorname{prox}_{σ F}`` & diff., ``\operatorname{prox}_{τ G^*}`` & diff., ``Λ``
 [Quasi-Newton Method](@ref quasiNewton) | [`quasi_Newton`](@ref), [`QuasiNewtonState`](@ref) | ``f``, ``\operatorname{grad} f`` |
 [Steihaug-Toint Truncated Conjugate-Gradient Method](@ref tCG) | [`truncated_conjugate_gradient_descent`](@ref), [`TruncatedConjugateGradientState`](@ref) | ``f``, ``\operatorname{grad} f``, ``\operatorname{Hess} f`` |
-[Subgradient Method](@ref SubgradientSolver) | [`subgradient_method`](@ref), [`SubGradientMethodState`](@ref) | ``f``, ``∂ f`` |
+[Subgradient Method](@refsec-subgradient-method) | [`subgradient_method`](@ref), [`SubGradientMethodState`](@ref) | ``f``, ``∂ f`` |
 [Stochastic Gradient Descent](@ref StochasticGradientDescentSolver) | [`stochastic_gradient_descent`](@ref), [`StochasticGradientDescentState`](@ref) | ``f = \sum_i f_i``, ``\operatorname{grad} f_i`` |
 [The Riemannian Trust-Regions Solver](@ref trust_regions) | [`trust_regions`](@ref), [`TrustRegionsState`](@ref) | ``f``, ``\operatorname{grad} f``, ``\operatorname{Hess} f`` |
 

diff --git a/docs/src/solvers/subgradient.md b/docs/src/solvers/subgradient.md
@@ -1,4 +1,4 @@
-# [Subgradient Method](@id SubgradientSolver)
+# [Subgradient method](@idsec-subgradient-method)
 
 ```@docs
 subgradient_method

diff --git a/docs/styles/Vocab/Manopt/accept.txt b/docs/styles/Vocab/Manopt/accept.txt
@@ -1,7 +1,6 @@
 Absil
 Adagrad
-Adjoint
-adjoint
+[A|a]djoint
 Armijo
 Bergmann
 Chambolle
@@ -26,14 +25,11 @@ Lanczos
 LineSearches.jl
 Manifolds.jl
 ManifoldsBase.jl
-manopt
-manopt.org
-Manopt
-Manopt.jl
+[Mm]anopt(:?.org|.jl)?
 Munkvold
 Mead
 Nelder
-parametrising
+[Pp]arametrising
 Parametrising
 Pock
 preconditioner