[release-0.18] Fix objective constant bug in conic problems (#1727)

* Fix objective constant bug in conic problems

* [ci skip] handle constant verbosely for clarity

* Update sdp.jl

src/solvers.jl

@@ -269,12 +269,13 @@ function solve(m::Model; suppress_warnings=false,
         end
     end
 
-    # The MathProgBase interface defines a conic problem to always be
-    # a minimization problem, so we need to flip the objective before
-    # reporting it to the user
+    # The MathProgBase interface defines a conic problem to always be a
+    # minimization problem, so we need to flip the objective before reporting it
+    # to the user. We also need to account for the objective constant which was
+    # added above by subtracting it prior to the flip and then re-adding it.
     if traits.conic && m.objSense == :Max
-        m.objBound *= -1
-        m.objVal *= -1
+        m.objBound = -1 * (m.objBound - m.obj.aff.constant) + m.obj.aff.constant
+        m.objVal = -1 * (m.objVal - m.obj.aff.constant) + m.obj.aff.constant
     end
 
     # If the solver was initially not set, we will restore this status

test/sdp.jl

@@ -770,4 +770,32 @@ ispsd(x::JuMP.JuMPArray) = ispsd(x.innerArray)
         @test norm(getvalue(X)) < 1e-5
         @test isapprox(getdual(X), Matrix(1.0I, 3, 3), atol=1e-5)
     end
+
+    @testset "Objective constants with $solver" for solver in sdp_solvers
+        # Test handling of constants in the objective. See JuMP issue #1390.
+        @testset "Minimize" begin
+            model = Model(solver = solver)
+            @variable(model, Xs1[1:3, 1:3], SDP)
+            @variable(model, Xs2[1:1, 1:1], SDP)
+            @variable(model, Xs3[1:1, 1:1], SDP)
+            @constraint(model, Xs1[1, 1] == 1)
+            @constraint(model, Xs2[1, 1] + Xs1[2, 2] + Xs1[3, 3] == 4)
+            @constraint(model, Xs3[1, 1] - Xs1[2, 1] - Xs1[3, 1] == 0)
+            @objective(model, Min, -Xs1[1, 3] + 0.5)
+            @test solve(model) == :Optimal
+            @test isapprox(getobjectivevalue(model), -1.5000, atol=1e-3)
+        end
+        @testset "Maximize" begin
+            model = Model(solver = solver)
+            @variable(model, Xs1[1:3, 1:3], SDP)
+            @variable(model, Xs2[1:1, 1:1], SDP)
+            @variable(model, Xs3[1:1, 1:1], SDP)
+            @constraint(model, Xs1[1, 1] == 1)
+            @constraint(model, Xs2[1, 1] + Xs1[2, 2] + Xs1[3, 3] == 4)
+            @constraint(model, Xs3[1, 1] - Xs1[2, 1] - Xs1[3, 1] == 0)
+            @objective(model, Max, -Xs1[1, 3] + 0.5)
+            @test solve(model) == :Optimal
+            @test isapprox(getobjectivevalue(model), 1.9142, atol=1e-3)
+        end
+    end
 end