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Refine docs.
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kellertuer committed Jul 8, 2024
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9 changes: 5 additions & 4 deletions src/solvers/interior_point_Newton.jl
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Expand Up @@ -41,12 +41,13 @@ The interior point Newton method iteratively solves ``F(p, μ, λ, s) = 0`` such
by a Newton method, that is
```math
\operatorname{grad} F(p, μ, λ, s)[X, Y, Z, W] = -F(p, μ, λ, s),
\operatorname{Jacobian} F(p, μ, λ, s)[X, Y, Z, W] = -F(p, μ, λ, s),
\text{ where }
X ∈ T_p\mathcal M, Y,W ∈ ℝ^m, Z ∈ ℝ^n
X ∈ T_p\mathcal M, Y,W ∈ ℝ^m, Z ∈ ℝ^n,
```
together denote the new search direction.
This can for example be done in the reduced form.
see [`CondensedKKTVectorFieldJacobian`](@ref) and [`CondensedKKTVectorField`](@ref), respectively,
for the reduced form, this is usually solved in.
From the resulting `X` and `Z` in the reeuced form, the other two can be computed.
Note that since the vector field ``F`` includes the gradients of the constraint
functions ``g,h`, its gradient or Jacobian requires the Hessians of the constraints.
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