Fix bug in setting a negative lower bound of a SOC constrained variab…

…le with `add_constraints` (#302)

* Adds a test uncovering a bug in SOC constraints. The bug was that defining a negative lower bound on the `t` variable of a SOC constraint by means of `add_constraints` (GreaterThan) silently corrupted the related `VariableInfo` object, but using `add_constraint` worked.

* Solves the bug in SOC constraints. The one uncovered by the test added in the last commit. The bug is solved by reworking many methods to work correctly with batch/vector (that is where the bug appeared) and changing single-element methods to wrap arguments and call the batch/vector variant. This way there will exist no difference in behavior between single-element and batch methods.

* Replace our solution by the one proposed by @odow

src/MOI_wrapper.jl

@@ -1091,8 +1091,12 @@ function _set_bounds(
         lower, upper = _bounds(s)
         info = _info(model, c)
         if lower !== nothing
-            push!(lower_columns, info.column)
-            push!(lower_values, lower)
+            if info.num_soc_constraints == 0
+                push!(lower_columns, info.column)
+                push!(lower_values, lower)
+            else
+                _set_variable_lower_bound(model, info, lower)
+            end
         end
         if upper !== nothing
             push!(upper_columns, info.column)

test/MOI/MOI_wrapper.jl

@@ -757,6 +757,31 @@ end
         MOI.optimize!(model)
         @test MOI.get(model, MOI.TerminationStatus()) == MOI.DUAL_INFEASIBLE
     end
+    @testset "negative post bound III" begin
+        # This test was added because add_constraint and add_constraints had
+        # different implementations and add_constraints failed where
+        # add_constraint succeeded.
+        MOI.empty!(model)
+        t = MOI.add_variable(model)
+        x = MOI.add_variables(model, 2)
+        c_soc = MOI.add_constraint(
+            model, MOI.VectorOfVariables([t; x]), MOI.SecondOrderCone(3)
+        )
+        c_lbs = MOI.add_constraints(
+            model, MOI.SingleVariable.([t; x]), MOI.GreaterThan.([-6.0, 3.0, 4.0])
+        )
+        c_lb = first(c_lbs)
+        MOI.set(model, MOI.ObjectiveFunction{MOI.SingleVariable}(), MOI.SingleVariable(t))
+        MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+        MOI.optimize!(model)
+        @test MOI.get(model, MOI.VariablePrimal(), t) == 5.0
+        MOI.delete(model, c_lb)
+        MOI.optimize!(model)
+        @test MOI.get(model, MOI.VariablePrimal(), t) == 5.0
+        MOI.delete(model, c_soc)
+        MOI.optimize!(model)
+        @test MOI.get(model, MOI.TerminationStatus()) == MOI.DUAL_INFEASIBLE
+    end
     @testset "2 SOC's" begin
         MOI.empty!(model)
         t = MOI.add_variable(model)