Deprecate in(x, ::Symbol) to create PSD constraint

docs/src/examples/general_examples/basic_usage.jl

@@ -88,7 +88,7 @@ p.optval
 x = Variable()
 y = Variable((2, 2))
 ## SDP constraints
-p = minimize(x + y[1, 1], isposdef(y), x >= 1, y[2, 1] == 1)
+p = minimize(x + y[1, 1], y ⪰ 0, x >= 1, y[2, 1] == 1)
 solve!(p, SCS.Optimizer; silent_solver = true)
 evaluate(y)
 

docs/src/examples/optimization_with_complex_variables/phase_recovery_using_MaxCut.jl

@@ -63,7 +63,7 @@ M = diagm(b) * (I(n) - A * A') * diagm(b)
 U = ComplexVariable(n, n)
 objective = inner_product(U, M)
 c1 = diag(U) == 1
-c2 = U in :SDP
+c2 = isposdef(U)
 p = minimize(objective, c1, c2)
 solve!(p, SCS.Optimizer; silent_solver = true)
 evaluate(U)

docs/src/examples/optimization_with_complex_variables/povm_simulation.jl

@@ -40,7 +40,7 @@ function get_visibility(K)
     P = [[ComplexVariable(2, 2) for i in 1:2] for j in 1:6]
     q = Variable(6, Positive())
     t = Variable(1, Positive())
-    constraints = [P[i][j] in :SDP for i in 1:6 for j in 1:2]
+    constraints = [isposdef(P[i][j]) for i in 1:6 for j in 1:2]
     constraints += sum(q) == 1
     constraints += t <= 1
     constraints += [P[i][1] + P[i][2] == q[i] * I(2) for i in 1:6]

docs/src/examples/optimization_with_complex_variables/power_flow_optimization.jl

@@ -20,7 +20,7 @@ c1 = Constraint[];
 for i in 2:n
     push!(c1, sum(W[i, :] .* (Y[i, :]')) == inj[i])
 end
-c2 = W in :SDP
+c2 = isposdef(W)
 c3 = real(W[1, 1]) == 1.06^2;
 push!(c1, c2)
 push!(c1, c3)

docs/src/manual/complex-domain_optimization.md

@@ -95,9 +95,11 @@ using Convex, SCS
 A = [ 0.47213595 0.11469794+0.48586827im; 0.11469794-0.48586827im  0.52786405]
 B = ComplexVariable(2, 2)
 ρ = kron(A, B)
-constraints = [partialtrace(ρ, 1, [2; 2]) == [1 0; 0 0]
-               tr(ρ) == 1
-               ρ in :SDP]
+constraints = [
+    partialtrace(ρ, 1, [2; 2]) == [1 0; 0 0],
+    tr(ρ) == 1,
+    isposdef(ρ),
+  ]
 p = satisfy(constraints)
 solve!(p, SCS.Optimizer; silent_solver = true)
 p.status

docs/src/manual/types.md

@@ -107,7 +107,7 @@ x = Variable(3, 3)
 y = Variable(3, 1)
 z = Variable()
 # constrain [x y; y' z] to be positive semidefinite
-constraint = ([x y; y' z] in :SDP)
+constraint = isposdef([x y; y' z])
 # or equivalently,
 constraint = ([x y; y' z] ⪰ 0)
 ```

src/Convex.jl

@@ -49,7 +49,6 @@ export conv,
     lieb_ando,
     # Constraints
     Constraint,
-    isposdef,
     ⪰,
     ⪯,
     socp,
@@ -99,6 +98,7 @@ for k in (
     :dot,
     :eigmax,
     :eigmin,
+    :isposdef,
     :logdet,
     :norm,
     :norm2,

src/constraints/PositiveSemidefiniteConeConstraint.jl

@@ -54,14 +54,7 @@ function populate_dual!(
     return
 end
 
-# TODO: Remove isposdef, change tests to use in. Update documentation and
-# notebooks
-LinearAlgebra.isposdef(x::AbstractExpr) = in(x, :SDP)
-
-function Base.in(x::AbstractExpr, y::Symbol)
-    if !(y in (:semidefinite, :SDP))
-        error("Set $y not understood")
-    end
+function LinearAlgebra.isposdef(x::AbstractExpr)
     if iscomplex(x)
         return PositiveSemidefiniteConeConstraint(
             [real(x) -imag(x); imag(x) real(x)],
@@ -70,20 +63,20 @@ function Base.in(x::AbstractExpr, y::Symbol)
     return PositiveSemidefiniteConeConstraint(x)
 end
 
-⪰(x::AbstractExpr, y::AbstractExpr) = in(x - y, :SDP)
+⪰(x::AbstractExpr, y::AbstractExpr) = isposdef(x - y)
 
 function ⪰(x::AbstractExpr, y::Value)
     if all(y .== 0)
-        return in(x, :SDP)
+        return isposdef(x)
     end
-    return in(x - constant(y), :SDP)
+    return isposdef(x - constant(y))
 end
 
 function ⪰(x::Value, y::AbstractExpr)
     if all(x .== 0)
-        return in(-y, :SDP)
+        return isposdef(-y)
     end
-    return in(constant(x) - y, :SDP)
+    return isposdef(constant(x) - y)
 end
 
 ⪯(x::AbstractExpr, y::AbstractExpr) = ⪰(y, x)

src/deprecations.jl

@@ -37,3 +37,15 @@ Base.:>(lhs::Value, rhs::AbstractExpr) = >(constant(lhs), rhs)
 @deprecate get_vectorized_size(x::AbstractExpr) length(x)
 
 @deprecate operatornorm(x::AbstractExpr) LinearAlgebra.opnorm(x)
+
+function Base.in(x::AbstractExpr, y::Symbol)
+    if !(y in (:semidefinite, :SDP))
+        error("Set $y not understood")
+    end
+    @warn(
+        "Using `x in $y` to construct a semidefinite constraint is " *
+        "deprecated. Use `isposdef(x)` or `x ⪰ 0` instead.",
+        maxlog = 1,
+    )
+    return isposdef(x)
+end

src/problem_depot/problems/sdp.jl

@@ -72,14 +72,7 @@ end
 ) where {T,test}
     x = Variable(Positive())
     y = Variable((3, 3))
-    p = minimize(
-        x + y[1, 1],
-        LinearAlgebra.isposdef(y),
-        x >= 1,
-        y[2, 1] == 1;
-        numeric_type = T,
-    )
-
+    p = minimize(x + y[1, 1], y ⪰ 0, x >= 1, y[2, 1] == 1; numeric_type = T)
     # @fact problem_vexity(p) --> ConvexVexity()
     handle_problem!(p)
     if test
@@ -425,7 +418,7 @@ end
     constraints = [
         partialtrace(ρ, 1, [2; 2]) ==
         [0.09942819 0.29923607; 0.29923607 0.90057181],
-        ρ in :SDP,
+        isposdef(ρ),
     ]
     p = satisfy(constraints; numeric_type = T)
 
@@ -658,7 +651,7 @@ end
     A = A + A' # now A is hermitian
     x = ComplexVariable(n, n)
     objective = sumsquares(A - x)
-    c1 = x in :SDP
+    c1 = isposdef(x)
     p = minimize(objective, c1; numeric_type = T)
 
     handle_problem!(p)

test/test_utilities.jl

@@ -958,6 +958,13 @@ function test_deprecation_norm()
     return
 end
 
+function test_deprecation_in_symbol()
+    x = Variable(2, 2)
+    @test_logs (:warn,) (x in :SDP)
+    @test in(x, :semidefinite) isa Convex.PositiveSemidefiniteConeConstraint
+    return
+end
+
 function test_dcp_rules()
     vexities = (
         Convex.ConcaveVexity(),