diff --git a/pyomo/solvers/plugins/solvers/cplex_direct.py b/pyomo/solvers/plugins/solvers/cplex_direct.py
index badca14f825..eb74f513c76 100644
--- a/pyomo/solvers/plugins/solvers/cplex_direct.py
+++ b/pyomo/solvers/plugins/solvers/cplex_direct.py
@@ -549,8 +549,6 @@ def _set_objective(self, obj):
             self._vars_referenced_by_obj = ComponentSet()
             self._objective = None
 
-        self._solver_model.objective.set_linear([(i, 0.0) for i in range(len(self._pyomo_var_to_solver_var_map.values()))])
-
         if obj.active is False:
             raise ValueError('Cannot add inactive objective to solver.')
 
@@ -571,12 +569,33 @@ def _set_objective(self, obj):
         self._solver_model.objective.set_sense(sense)
         if hasattr(self._solver_model.objective, 'set_offset'):
             self._solver_model.objective.set_offset(cplex_expr.offset)
-        if len(cplex_expr.coefficients) != 0:
-            self._solver_model.objective.set_linear(list(zip(cplex_expr.variables, cplex_expr.coefficients)))
-        if len(cplex_expr.q_coefficients) != 0:
-            self._solver_model.objective.set_quadratic_coefficients(list(zip(cplex_expr.q_variables1,
-                                                                             cplex_expr.q_variables2,
-                                                                             cplex_expr.q_coefficients)))
+
+        linear_objective_already_exists = any(self._solver_model.objective.get_linear())
+        quadratic_objective_already_exists = self._solver_model.objective.get_num_quadratic_nonzeros()
+
+        contains_linear_terms = any(cplex_expr.coefficients)
+        contains_quadratic_terms = any(cplex_expr.q_coefficients)
+        num_cols = len(self._pyomo_var_to_solver_var_map)
+
+        if linear_objective_already_exists or contains_linear_terms:
+            self._solver_model.objective.set_linear([(i, 0.0) for i in range(num_cols)])
+
+            if contains_linear_terms:
+                self._solver_model.objective.set_linear(list(zip(cplex_expr.variables, cplex_expr.coefficients)))
+
+        if quadratic_objective_already_exists or contains_quadratic_terms:
+            self._solver_model.objective.set_quadratic([0] * num_cols)
+
+            if contains_quadratic_terms:
+                self._solver_model.objective.set_quadratic_coefficients(
+                    list(
+                        zip(
+                            cplex_expr.q_variables1,
+                            cplex_expr.q_variables2,
+                            cplex_expr.q_coefficients
+                        )
+                    )
+                )
         self._objective = obj
         self._vars_referenced_by_obj = referenced_vars
 
diff --git a/pyomo/solvers/tests/checks/test_CPLEXPersistent.py b/pyomo/solvers/tests/checks/test_CPLEXPersistent.py
new file mode 100644
index 00000000000..51ff1ab7e43
--- /dev/null
+++ b/pyomo/solvers/tests/checks/test_CPLEXPersistent.py
@@ -0,0 +1,35 @@
+import pyutilib.th as unittest
+
+from pyomo.environ import *
+from pyomo.opt import *
+
+try:
+    import cplex
+
+    cplexpy_available = True
+except ImportError:
+    cplexpy_available = False
+
+
+@unittest.skipIf(not cplexpy_available, "The 'cplex' python bindings are not available")
+class TestQuadraticObjective(unittest.TestCase):
+    def test_quadratic_objective_is_set(self):
+        model = ConcreteModel()
+        model.X = Var(bounds=(-2, 2))
+        model.Y = Var(bounds=(-2, 2))
+        model.O = Objective(expr=model.X ** 2 + model.Y ** 2)
+        model.C1 = Constraint(expr=model.Y >= 2 * model.X - 1)
+        model.C2 = Constraint(expr=model.Y >= -model.X + 2)
+        opt = SolverFactory("cplex_persistent")
+        opt.set_instance(model)
+        opt.solve()
+
+        self.assertAlmostEqual(model.X.value, 1, places=3)
+        self.assertAlmostEqual(model.Y.value, 1, places=3)
+
+        del model.O
+        model.O = Objective(expr=model.X ** 2)
+        opt.set_objective(model.O)
+        opt.solve()
+        self.assertAlmostEqual(model.X.value, 0, places=3)
+        self.assertAlmostEqual(model.Y.value, 2, places=3)