Use ProductManifold instead of × (#541)

* use ProductManifold instead of ×
* format
* fix docstring of ConstrainedManifoldObjective
* fix docstring of ConstrainedManoptProblem
* fix math in docstring of ConstrainedManifoldObjective
* fix missing backticks

Author: JoshuaLampert

src/plans/constrained_plan.jl

@@ -55,11 +55,11 @@ get_parameter(acsf::AbstractConstrainedSlackFunctor, ::Val{:β}) = acsf.β
 
 Describes the constrained objective
 ```math
-\begin{aligned}
+\\begin{aligned}
  $(_tex(:argmin))_{p ∈ } & f(p)\\
  $(_tex(:text, "subject to")) & g_i(p) ≤ 0 $(_tex(:quad)) $(_tex(:text, "for all ")) i=1,…,m,\\
  $(_tex(:quad)) &h_j(p)=0 $(_tex(:quad)) $(_tex(:text, "for all ")) j=1,…,n.
-\end{aligned}
+\\end{aligned}
 ```
 
 # Fields
@@ -72,7 +72,7 @@ Describes the constrained objective
 ``h: $(_math(:M)) → ℝ^n`` also possibly containing its gradient and/or Hessian
 
 # Constructors
-    ConstrainedManifoldObjective(M::AbstractManifold, f, grad_f;
+    ConstrainedManifoldObjective(f, grad_f;
         g=nothing,
         grad_g=nothing,
         h=nothing,
@@ -94,7 +94,7 @@ of the ranges of `h` and `g`, respectively.
 You can also provide a manifold `M` and a point `p` to use one evaluation of the constraints
 to automatically try to determine these sizes.
 
-    ConstrainedManifoldObjective(M::AbstractManifold, mho::AbstractManifoldObjective;
+    ConstrainedManifoldObjective(mho::AbstractManifoldObjective;
         equality_constraints = nothing,
         inequality_constraints = nothing
     )
@@ -305,7 +305,7 @@ function ConstrainedManifoldObjective(
 end
 
 @doc """
-    ConstrainedProblem{
+    ConstrainedManoptProblem{
         TM <: AbstractManifold,
         O <: AbstractManifoldObjective
         HR<:Union{AbstractPowerRepresentation,Nothing},

src/plans/constrained_set_plan.jl

@@ -14,7 +14,7 @@ where ``$(_tex(:Cal, "C")) ⊂ $(_math(:M))`` is a convex closed subset.
 * `objective::AbstractManifoldObjective` the (unconstrained) objective, which
   contains ``f`` and for example ist gradient ``$(_tex(:grad)) f``.
 * `project!!::PF` a projection function ``$(_tex(:proj))_{$(_tex(:Cal, "C"))}: $(_math(:M)) → $(_tex(:Cal, "C"))`` that projects onto the set ``$(_tex(:Cal, "C"))``.
-* `indicator::IF` the indicator function ``ι_{$(_tex(:Cal, "C"))}(p) = $(_tex(:cases, "0 &" * _tex(:text, " for ") * "p∈" * _tex(:Cal, "C"), "∞ &" * _tex(:text, " else.")))
+* `indicator::IF` the indicator function ``ι_{$(_tex(:Cal, "C"))}(p) = $(_tex(:cases, "0 &" * _tex(:text, " for ") * "p∈" * _tex(:Cal, "C"), "∞ &" * _tex(:text, " else.")))``
 
 # Constructor
 

src/plans/interior_point_Newton_plan.jl

@@ -1012,7 +1012,12 @@ function calculate_σ(
         λ,
         s;
         vector_space = Rn,
-        N = M × vector_space(length(μ)) × vector_space(length(λ)) × vector_space(length(s)),
+        N = ProductManifold(
+            M,
+            vector_space(length(μ)),
+            vector_space(length(λ)),
+            vector_space(length(s)),
+        ),
         q = allocate_result(N, rand),
     )
     q1, q2, q3, q4 = submanifold_components(N, q)

src/solvers/interior_point_Newton.jl

@@ -187,8 +187,12 @@ function interior_point_Newton!(
         step_objective = ManifoldGradientObjective(
             KKTVectorFieldNormSq(cmo), KKTVectorFieldNormSqGradient(cmo); evaluation = evaluation
         ),
-        _step_M::AbstractManifold = M × vector_space(length(μ)) × vector_space(length(λ)) ×
+        _step_M::AbstractManifold = ProductManifold(
+            M,
+            vector_space(length(μ)),
+            vector_space(length(λ)),
             vector_space(length(s)),
+        ),
         step_problem = DefaultManoptProblem(_step_M, step_objective),
         _step_p = rand(_step_M),
         step_state = StepsizeState(_step_p, zero_vector(_step_M, _step_p)),
@@ -204,7 +208,7 @@ function interior_point_Newton!(
         ),
         stopping_criterion::StoppingCriterion = StopAfterIteration(800) |
             StopWhenKKTResidualLess(1.0e-8),
-        _sub_M = M × vector_space(length(λ)),
+        _sub_M = ProductManifold(M, vector_space(length(λ))),
         _sub_p = rand(_sub_M),
         _sub_X = rand(_sub_M; vector_at = _sub_p),
         sub_objective = decorate_objective!(