Add example (#23)

* Add example

* Fix format

* Add JuliaFormatter v2

Author: blegat

.github/workflows/format_check.yml

@@ -18,7 +18,7 @@ jobs:
         shell: julia --color=yes {0}
         run: |
           using Pkg
-          Pkg.add(PackageSpec(name="JuliaFormatter", version="1"))
+          Pkg.add(PackageSpec(name="JuliaFormatter", version="2"))
           using JuliaFormatter
           format(".", verbose=true)
           out = String(read(Cmd(`git diff`)))

README.md

@@ -14,3 +14,58 @@ Extends MathOptInterface (MOI) to low-rank constraints.
 See "Why you should stop using the monomial basis" at [JuMP-dev 2024](https://jump.dev/meetings/jumpdev2024/) : [slides](https://jump.dev/assets/jump-dev-workshops/2024/legat.html) [video](https://youtu.be/CGPHaHxCG2w)
 
 Started as an [MOI issue](https://github.com/jump-dev/MathOptInterface.jl/issues/2197) and [MOI PR](https://github.com/jump-dev/MathOptInterface.jl/pull/2198).
+
+## Use with JuMP
+
+To use LowRankOpt with [JuMP](https://github.com/jump-dev/JuMP.jl), use
+add its bridge to your model with:
+```julia
+model = Model()
+LRO.add_all_bridges(model, Float64)
+```
+Then, either use the `LRO.SetDotProducts` or `LRO.LinearCombinationInSet`.
+[Check with `print_active_bridges(model)`](https://jump.dev/JuMP.jl/stable/tutorials/conic/ellipse_approx/)
+to see if the solver receives the low-rank constraint or if it is transformed to classical constraints.
+The solvers that support `LRO.SetDotProducts` are:
+* [DSDP.jl](https://github.com/jump-dev/DSDP.jl/pull/37), [Hypatia.jl](https://github.com/jump-dev/Hypatia.jl/pull/844), [SDPLR.jl](https://github.com/jump-dev/SDPLR.jl/pull/26)
+The solvers that support `LRO.LinearCombinationInSet` are:
+* [Hypatia.jl](https://github.com/jump-dev/Hypatia.jl/pull/844)
+If you use `LRO.LinearCombinationInSet` while the solvers supports `LRO.SetDotProducts` or vice versa, simply [use a `Dualization.jl` layer](https://jump.dev/JuMP.jl/stable/tutorials/conic/dualization/).
+
+Note that `Hypatia.jl` only supports `LRO.SetDotProducts{LRO.WITHOUT_SET}` or `LRO.LinearCombinationInSet{LRO.WITHOUT_SET}` and not the `LRO.WITH_SET` version.
+
+## Example
+
+Below is [this example](https://github.com/jump-dev/SDPLR.jl?tab=readme-ov-file#example-modifying-the-rank-and-checking-optimality)
+adapted to exploit the low-rank constraints.
+
+```julia-repl
+julia> include(joinpath(dirname(dirname(pathof(LowRankOpt))), "examples", "maxcut.jl"))
+maxcut (generic function with 2 methods)
+
+julia> model = maxcut(weights, SDPLR.Optimizer);
+
+julia> optimize!(model)
+
+            ***   SDPLR 1.03-beta   ***
+
+===================================================
+ major   minor        val        infeas      time
+---------------------------------------------------
+    1        9   1.77916821e+02  2.0e+01       0
+    2       12  -1.78345610e+01  4.7e-01       0
+    3       14  -1.80546137e+01  2.5e-01       0
+    4       16  -1.80170234e+01  9.7e-02       0
+    5       18  -1.79967453e+01  4.0e-02       0
+    6       19  -1.79987069e+01  1.1e-02       0
+    7       20  -1.79999405e+01  1.7e-03       0
+    8       21  -1.79999841e+01  3.3e-04       0
+    9       22  -1.79999912e+01  5.9e-06       0
+===================================================
+
+DIMACS error measures: 5.86e-06 0.00e+00 0.00e+00 0.00e+00 2.25e-05 9.84e-06
+
+
+julia> objective_value(model)
+17.99998881724702
+```

examples/maxcut.jl

@@ -0,0 +1,25 @@
+using LinearAlgebra, JuMP, LowRankOpt
+
+function maxcut(weights, solver)
+    N = LinearAlgebra.checksquare(weights)
+    L = Diagonal(weights * ones(N)) - weights
+    model = Model(solver)
+    LRO.Bridges.add_all_bridges(backend(model).optimizer, Float64)
+    cone = MOI.PositiveSemidefiniteConeTriangle(N)
+    factors = LRO.TriangleVectorization.(
+        LRO.positive_semidefinite_factorization.(e_i.(1:N, N)),
+    )
+    set = LRO.SetDotProducts{LRO.WITH_SET}(cone, factors)
+    @variable(
+        model,
+        dot_prod_set[1:(length(factors)+MOI.dimension(cone))] in set
+    )
+    dot_prod = dot_prod_set[1:length(factors)]
+    X = reshape_vector(
+        dot_prod_set[length(factors) .+ (1:MOI.dimension(cone))],
+        SymmetricMatrixShape(N),
+    )
+    @objective(model, Max, dot(L, X) / 4)
+    @constraint(model, dot_prod .== 1)
+    return model
+end

test/Project.toml

@@ -3,4 +3,5 @@ FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LowRankOpt = "607ca3ad-272e-43c8-bcbe-fc71b56c935c"
 MathOptInterface = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
+SDPLR = "56161740-ea4e-4253-9d15-43c62ff94d95"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"