Add GenericConstraint{RelativeEntropyCone} support (#623)

Author: odow

src/atoms/RelativeEntropyAtom.jl

@@ -39,15 +39,15 @@ function evaluate(e::RelativeEntropyAtom)
 end
 
 function new_conic_form!(context::Context{T}, e::RelativeEntropyAtom) where {T}
-    # relative_entropy(x,y) = sum_i( x_i log (x_i/y_i) )
-    w = conic_form!(context, e.children[1])
-    v = conic_form!(context, e.children[2])
-    u = conic_form!(context, Variable())
-    f = operate(vcat, T, sign(e), u, v, w)
-    d = MOI.output_dimension(w)
-    @assert d == MOI.output_dimension(v)
-    MOI_add_constraint(context.model, f, MOI.RelativeEntropyCone(2d + 1))
-    return u
+    u = Variable()
+    x, y = e.children
+    # Convex.jl has the connvention:
+    #   u >= relative_entropy(x,y) = sum_i( x_i log (x_i/y_i) )
+    # But MOI has the reversed convention:
+    #   MOI.RelativeEntropyCone has the order (u, y, x)
+    f = vcat(u, y, x)
+    add_constraint!(context, GenericConstraint{MOI.RelativeEntropyCone}(f))
+    return conic_form!(context, u)
 end
 
 relative_entropy(x::AbstractExpr, y::AbstractExpr) = RelativeEntropyAtom(x, y)

src/constraints/GenericConstraint.jl

@@ -283,3 +283,16 @@ function vexity(vex, ::MOI.RotatedSecondOrderCone)
     end
     return ConvexVexity()
 end
+
+# ==============================================================================
+#     RelativeEntropyCone
+# ==============================================================================
+
+head(io::IO, ::MOI.RelativeEntropyCone) = print(io, "RelativeEntropyCone")
+
+function vexity(vex, ::MOI.RelativeEntropyCone)
+    if !(vex == ConstVexity() || vex == AffineVexity())
+        return NotDcp()
+    end
+    return ConvexVexity()
+end

test/test_atoms.jl

@@ -952,7 +952,7 @@ end
 
 function test_RelativeEntropyAtom()
     target = """
-    variables: w1, w2, v1, v2, u
+    variables: u, v1, v2, w1, w2
     minobjective: 1.0 * u + 0.0
     [1.0*u, 1.0*v1, 1.0*v2, 1.0*w1, 1.0*w2] in RelativeEntropyCone(5)
     """
@@ -962,7 +962,7 @@ function test_RelativeEntropyAtom()
         return relative_entropy(x, y)
     end
     target = """
-    variables: w1, w2, v1, v2, u
+    variables: u, v1, v2, w1, w2
     minobjective: -1.0 * u + 1.0
     [1.0*u, 1.0*v1, 1.0*v2, 1.0*w1, 1.0*w2] in RelativeEntropyCone(5)
     """

test/test_constraints.jl

@@ -279,6 +279,24 @@ function test_GenericConstraint_ExponentialConeConstraint()
     return
 end
 
+### constraints/GenericConstraint_RelativeEntropyCone
+
+function test_GenericConstraint_RelativeEntropyConeConstraint()
+    # u >= sum_i( w_i log (w_i/v_i) )
+    u = Variable()
+    v = [1, 2]
+    w = Variable(2)
+    c = Convex.GenericConstraint{MOI.RelativeEntropyCone}(vcat(u, v, w))
+    p = minimize(u, [c, w >= 2])
+    solve!(p, SCS.Optimizer; silent_solver = true)
+    @test isapprox(u.value, 2 * log(2 / 1) + 2 * log(2 / 2); atol = 1e-4)
+    @test isapprox(c.dual, [1, 2, 1, -log(2) - 1, -1]; atol = 1e-3)
+    c = Convex.GenericConstraint{MOI.RelativeEntropyCone}(vcat(square(u), 1, u))
+    @test vexity(c) === Convex.NotDcp()
+    @test sprint(Convex.head, c) == "RelativeEntropyCone"
+    return
+end
+
 end  # TestConstraints
 
 TestConstraints.runtests()