Add support for log-det through JuMP

src/MOI_wrapper.jl

@@ -157,11 +157,26 @@ function _expr(model::Optimizer, x::MOI.VariableIndex)
     return model.moi_to_convex[x]
 end
 
+function _expr(model::Optimizer, A::AbstractArray{MOI.VariableIndex})
+    return reshape(vcat([_expr(model, x) for x in vec(A)]...), size(A)...)
+end
+
 function _expr(model::Optimizer, f::MOI.AbstractScalarFunction)
     return _expr(model, convert(MOI.ScalarNonlinearFunction, f))
 end
 
 function _expr(model::Optimizer, f::MOI.ScalarNonlinearFunction)
+    # log(det(X)) is a single concave atom in Convex (logdet); det alone is not
+    # representable, so we recognise the composition here before generic
+    # recursion would fail on the unsupported `:det` head.
+    if f.head == :log &&
+       length(f.args) == 1 &&
+       f.args[1] isa MOI.ScalarNonlinearFunction &&
+       f.args[1].head == :det &&
+       length(f.args[1].args) == 1 &&
+       f.args[1].args[1] isa AbstractMatrix
+        return LinearAlgebra.logdet(_expr(model, f.args[1].args[1]))
+    end
     args = _expr.(model, f.args)
     if f.head == :+
         if length(args) == 1

test/MOI_wrapper.jl

@@ -9,7 +9,10 @@ using Test
 
 import Convex
 import ECOS
+import JuMP
+import LinearAlgebra
 import MathOptInterface as MOI
+import SCS
 import SparseArrays
 
 function runtests()
@@ -181,6 +184,28 @@ function test_not_dcp_objective_min()
     return
 end
 
+function test_log_det_objective_from_jump()
+    n = 2
+    model = JuMP.Model(() -> Convex.Optimizer(SCS.Optimizer))
+    JuMP.set_silent(model)
+    JuMP.@variable(model, X[1:n, 1:n], Symmetric)
+    JuMP.@constraint(model, X in JuMP.PSDCone())
+    JuMP.@constraint(model, LinearAlgebra.tr(X) <= 4)
+    op_det = JuMP.NonlinearOperator(LinearAlgebra.det, :det)
+    JuMP.@objective(model, Max, log(op_det(X)))
+    attr = MOI.ObjectiveFunction{MOI.ScalarNonlinearFunction}()
+    moi_f = MOI.get(model, attr)
+    @test moi_f.head == :log
+    @test moi_f.args[1] isa MOI.ScalarNonlinearFunction
+    @test moi_f.args[1].head == :det
+    @test moi_f.args[1].args[1] isa Matrix{MOI.VariableIndex}
+    JuMP.optimize!(model)
+    @test JuMP.termination_status(model) == MOI.OPTIMAL
+    # log det X is maximised on tr(X) ≤ 4, X ⪰ 0 by X = 2I, giving log det = 2 log 2
+    @test isapprox(JuMP.objective_value(model), 2 * log(2); atol = 1e-3)
+    return
+end
+
 end  # TestMOIWrapper
 
 TestMOIWrapper.runtests()

test/Project.toml

@@ -5,6 +5,7 @@ Clarabel = "61c947e1-3e6d-4ee4-985a-eec8c727bd6e"
 Convex = "f65535da-76fb-5f13-bab9-19810c17039a"
 ECOS = "e2685f51-7e38-5353-a97d-a921fd2c8199"
 GLPK = "60bf3e95-4087-53dc-ae20-288a0d20c6a6"
+JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MathOptInterface = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"