Initial infrastructure for Krylov-based linear solvers (#56)

* Initial infrastructure for Krylov-based linear solvers

* Add unit tests for krylov solvers

* Add SQD solver

* Add unit tests for SQD solvers

* Update docs

* Allow for user-specified tolerances

* Add compat entry for Krylov

* Krylov solver for symmetric indefinite systems

* Update docs and unify naming conventions

* Tighten default tolerances

Author: mtanneau

Project.toml

@@ -4,6 +4,7 @@ authors = ["Mathieu Tanneau <[email protected]>"]
 version = "0.5.1"
 
 [deps]
+Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
 LDLFactorizations = "40e66cde-538c-5869-a4ad-c39174c6795b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
@@ -15,6 +16,7 @@ SuiteSparse = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
+Krylov = "0.5.2"
 LDLFactorizations = "^0.5"
 MathOptInterface = "~0.9.5"
 QPSReader = "0.2"

docs/src/manual/linear_systems.md

@@ -38,7 +38,7 @@ The augmented system above can be reduced to the positive-definite _normal equat
 \Delta x &= (Θ^{-1} + R_{p})^{-1} (A^{T} \Delta y - \xi_{d})
 \end{array}
 ```
-When selected, this reduction is transparent to the interior-point algorithm.
+If available and when selected, this reduction is transparent to the interior-point algorithm.
 
 To enable the use of fast external libraries and/or specialized routines, the resolution of linear systems is performed by an [`AbstractKKTSolver`] object.
 
@@ -52,4 +52,11 @@ Here is a list of currently supported linear solvers:
 | [`Dense_SymPosDef`](@ref) | `Real` | Normal equations | Dense / LAPACK | Cholesky
 | [`Cholmod_SymQuasDef`](@ref) | `Float64` | Augmented system | CHOLMOD | LDLᵀ
 | [`Cholmod_SymPosDef`](@ref) | `Float64` | Normal equations | CHOLMOD | Cholesky
-| [`LDLFact_SymQuasDef`](@ref) | `Real` | Augmented system | [LDLFactorizations.jl](https://github.com/JuliaSmoothOptimizers/LDLFactorizations.jl) | LDLᵀ
+| [`LDLFact_SymQuasDef`](@ref) | `Real` | Augmented system | [LDLFactorizations.jl](https://github.com/JuliaSmoothOptimizers/LDLFactorizations.jl) | LDLᵀ
+| [`KrylovSPDSolver`](@ref) | `Real` | Normal equations | [Krylov.jl](https://github.com/JuliaSmoothOptimizers/Krylov.jl) | Krylov
+| [`KrylovSIDSolver`](@ref) | `Real` | Augmented system[^1] | [Krylov.jl](https://github.com/JuliaSmoothOptimizers/Krylov.jl) | Krylov
+| [`KrylovSQDSolver`](@ref) | `Real` | Augmented system[^1] | [Krylov.jl](https://github.com/JuliaSmoothOptimizers/Krylov.jl) | Krylov
+
+[^1]: [`KrylovSIDSolver`](@ref)s view the augmented system as a symmetric indefinite system,
+    while [`KrylovSQDSolver`](@ref)s exploit its 2x2 structure and quasi-definite property.
+    See the reference documentation for more details.

docs/src/reference/kkt_solvers.md

@@ -65,4 +65,23 @@ Cholmod_SymPosDef
 
 ```@docs
 LDLFact_SymQuasDef
+```
+
+## Krylov
+
+!!! warning
+    Iterative methods are still an experimental feature.
+    Some numerical and performance issues should be expected.
+
+
+```@docs
+KrylovSPDSolver
+```
+
+```@docs
+KrylovSIDSolver
+```
+
+```@docs
+KrylovSQDSolver
 ```

src/KKTSolver/KKTSolver.jl

@@ -107,6 +107,7 @@ include("test.jl")
 include("lapack.jl")
 include("cholmod.jl")
 include("ldlfact.jl")
+include("krylov.jl")
 
 """
     default_options(Tv)