Re-write KKT module

.gitignore

@@ -3,3 +3,9 @@
 *.jl.*.cov
 *.jl.mem
 Manifest.toml
+
+/app
+/dat
+/exp
+/.vscode
+/*.jl

Project.toml

@@ -1,11 +1,12 @@
 name = "Tulip"
 uuid = "6dd1b50a-3aae-11e9-10b5-ef983d2400fa"
 authors = ["Mathieu Tanneau <mathieu.tanneau@gmail.com>"]
-version = "0.7.5"
+version = "0.8.0"
 
 [deps]
 CodecBzip2 = "523fee87-0ab8-5b00-afb7-3ecf72e48cfd"
 CodecZlib = "944b1d66-785c-5afd-91f1-9de20f533193"
+Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
 LDLFactorizations = "40e66cde-538c-5869-a4ad-c39174c6795b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearOperators = "5c8ed15e-5a4c-59e4-a42b-c7e8811fb125"
@@ -21,6 +22,7 @@ TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 [compat]
 CodecBzip2 = "0.7.2"
 CodecZlib = "0.7.0"
+Krylov = "0.7.3"
 LDLFactorizations = "0.6, 0.7, 0.8"
 LinearOperators = "2.0"
 MathOptInterface = "0.9.5"

docs/make.jl

@@ -1,17 +1,19 @@
 using Documenter, Tulip
 
+const _FAST = findfirst(isequal("--fast"), ARGS) !== nothing
+
 makedocs(
     sitename = "Tulip.jl",
     authors = "Mathieu Tanneau",
     format = Documenter.HTML(prettyurls = get(ENV, "CI", nothing) == "true"),
+    doctest = !_FAST,
     pages = [
         "Home" => "index.md",
         "Tutorials" => Any[
             "tutorials/lp_example.md",
         ],
         "User manual" => Any[
             "Problem formulation" => "manual/formulation.md",
-            "Solving linear systems" => "manual/linear_systems.md",
             "Algorithms" => Any[
                 "Homogeneous Self-Dual" => "manual/IPM/HSD.md",
                 "Predictor-Corrector" => "manual/IPM/MPC.md"
@@ -20,7 +22,13 @@ makedocs(
         ],
         "Reference" => Any[
             "Presolve" => "reference/Presolve/presolve.md",
-            "KKT solvers" => "reference/KKT/kkt_solvers.md",
+            "KKT" => [
+                "reference/KKT/kkt.md",
+                "reference/KKT/tlp_cholmod.md",
+                "reference/KKT/tlp_dense.md",
+                "reference/KKT/tlp_krylov.md",
+                "reference/KKT/tlp_ldlfact.md",
+            ],
             "Julia API" => "reference/API.md",
             "Attributes" => "reference/attributes.md",
             "Options" => "reference/options.md"
@@ -30,4 +38,4 @@ makedocs(
 
 deploydocs(
     repo = "github.com/ds4dm/Tulip.jl.git"
-)
+)

docs/src/reference/KKT/kkt.md

@@ -0,0 +1,77 @@
+```@meta
+CurrentModule = Tulip.KKT
+```
+
+# Overview
+
+The `KKT` module provides a modular, customizable interface for developing and selecting various approaches to solve the KKT systems.
+
+## KKT backends
+
+```@docs
+AbstractKKTBackend
+```
+
+```@docs
+DefaultKKTBackend
+```
+
+## KKT systems
+
+All formulations below refer to a linear program in primal-dual standard form
+```math
+    \begin{array}{rl}
+    (P) \ \ \ 
+    \displaystyle \min_{x}
+    & c^{\top} x\\
+    s.t.
+    & A x = b\\
+    & l \leq x \leq u
+    \end{array}
+    \quad \quad \quad
+    \begin{array}{rl}
+    (D) \ \ \ 
+    \displaystyle \max_{y, z}
+    & b^{\top} y + l^{\top}z^{l} - u^{\top}z^{u}\\
+    s.t.
+    & A^{\top}y + z^{l} - z^{u} = c\\
+    & z^{l}, z^{u} \geq 0
+    \end{array}
+```
+
+```@docs
+AbstractKKTSystem
+```
+
+```@docs
+DefaultKKTSystem
+```
+
+```@docs
+K2
+```
+
+```@docs
+K1
+```
+
+## KKT solvers
+
+```@docs
+AbstractKKTSolver
+```
+
+Custom linear solvers should (preferably) inherit from the `AbstractKKTSolver` class,
+and extend the following functions:
+
+```@docs
+setup
+```
+
+```@docs
+update!
+```
+
+```@docs
+solve!
+```

docs/src/reference/KKT/tlp_cholmod.md

@@ -0,0 +1,13 @@
+```@meta
+CurrentModule = Tulip.KKT
+```
+
+# TlpCholmod
+
+```@docs
+TlpCholmod.Backend
+```
+
+```@docs
+TlpCholmod.CholmodSolver
+```

docs/src/reference/KKT/tlp_dense.md

@@ -0,0 +1,13 @@
+```@meta
+CurrentModule = Tulip.KKT.TlpDense
+```
+
+# TlpDense
+
+```@docs
+TlpDense.Backend
+```
+
+```@docs
+TlpDense.DenseSolver
+```

docs/src/reference/KKT/tlp_krylov.md

@@ -0,0 +1,30 @@
+```@meta
+CurrentModule = Tulip.KKT.TlpKrylov
+```
+
+# TlpKrylov
+
+!!! warning
+    Iterative methods are still an experimental feature.
+    Some numerical and performance issues should be expected.
+
+
+```@docs
+TlpKrylov.Backend
+```
+
+```@docs
+TlpKrylov.AbstractKrylovSolver
+```
+
+```@docs
+TlpKrylov.SPDSolver
+```
+
+```@docs
+TlpKrylov.SIDSolver
+```
+
+```@docs
+TlpKrylov.SQDSolver
+```

docs/src/reference/KKT/tlp_ldlfact.md

@@ -0,0 +1,13 @@
+```@meta
+CurrentModule = Tulip.KKT.TlpLDLFactorizations
+```
+
+# TlpLDLFactorizations
+
+```@docs
+TlpLDLFactorizations.Backend
+```
+
+```@docs
+TlpLDLFactorizations.LDLFactSolver
+```