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[KKT] Fix symmetric K3 formulation #345

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Jun 13, 2024
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[KKT] Fix symmetric K3 formulation #345

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16 changes: 9 additions & 7 deletions src/KKT/KKTsystem.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -14,12 +14,12 @@ conditions at the current primal-dual iterate ``(x, s, y, z, ν, w)``.

The associated matrix is
```
[Wₓₓ 0 Aₑ' Aᵢ' -I 0 ] [Δx]
[ 0 0 0 -I 0 -I ] [Δs]
[Aₑ 0 0 0 0 0 ] [Δy]
[Aᵢ -I 0 0 0 0 ] [Δz]
[V 0 0 0 X 0 ] [Δν]
[0 W 0 0 0 S ] [Δw]
[Wₓₓ 0 Aₑ' Aᵢ' V½ 0 ] [Δx]
[0 0 0 -I 0 W½ ] [Δs]
[Aₑ 0 0 0 0 0 ] [Δy]
[Aᵢ -I 0 0 0 0 ] [Δz]
[V½ 0 0 0 -X 0 ] [Δτ]
[0 W½ 0 0 0 -S ] [Δρ]
```
with
* ``Wₓₓ``: Hessian of the Lagrangian.
Expand All @@ -29,6 +29,8 @@ with
* ``S = diag(s)``
* ``V = diag(ν)``
* ``W = diag(w)``
* ``Δτ = -W^{-½}Δν``
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* ``Δρ = -W^{-½}Δw``
"""
abstract type AbstractUnreducedKKTSystem{T, VT, MT, QN} <: AbstractKKTSystem{T, VT, MT, QN} end

Expand All @@ -42,7 +44,7 @@ the two last rows associated to the bounds' duals ``(ν, w)``.
At a primal-dual iterate ``(x, s, y, z)``, the matrix writes
```
[Wₓₓ + Σₓ 0 Aₑ' Aᵢ'] [Δx]
[ 0 Σₛ 0 -I ] [Δs]
[0 Σₛ 0 -I ] [Δs]
[Aₑ 0 0 0 ] [Δy]
[Aᵢ -I 0 0 ] [Δz]
```
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