Fix more math typos (#542)

* Simplify formula display by using the global constrained problem string.
* Update changelog.

Author: kellertuer

Changelog.md

@@ -10,6 +10,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Fixed
 
+* Change the construction of the product manifold in `interior_point_newton` from `×` to `ProductManifold`, so that the algorithm also work on Product manifolds `M`, where it now correctly wraps `M` instead of extending it.
+* unifies the doc strings for constrained problems
 * fixes a few typos in the doc strings of matrix update formulae within the quasi-Newton and CG solver.
 
 ## [0.5.27] November 11, 2025

src/plans/constrained_plan.jl

@@ -50,26 +50,21 @@ function set_parameter!(
 end
 get_parameter(acsf::AbstractConstrainedSlackFunctor, ::Val{:β}) = acsf.β
 
-@doc """
+"""
     ConstrainedManifoldObjective{T<:AbstractEvaluationType, C<:ConstraintType} <: AbstractManifoldObjective{T}
 
-Describes the constrained objective
-```math
-\\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)) $(_tex(:text, "for all ")) j=1,…,n.
-\\end{aligned}
-```
+Describes a constrained objective
+
+$(_problem(:Constrained))
 
 # Fields
 
 * `objective`: an [`AbstractManifoldObjective`](@ref) representing the unconstrained
   objective, that is containing cost ``f``, the gradient of the cost ``f`` and maybe the Hessian.
 * `equality_constraints`: an [`AbstractManifoldObjective`](@ref) representing the equality constraints
 ``h: $(_math(:M)) → ℝ^n`` also possibly containing its gradient and/or Hessian
-* `equality_constraints`: an [`AbstractManifoldObjective`](@ref) representing the equality constraints
-``h: $(_math(:M)) → ℝ^n`` also possibly containing its gradient and/or Hessian
+* `inequality_constraints`: an [`AbstractManifoldObjective`](@ref) representing the inequality constraints
+``g: $(_math(:M)) → ℝ^m`` also possibly containing its gradient and/or Hessian
 
 # Constructors
     ConstrainedManifoldObjective(f, grad_f;