diff --git a/jaxopt/_src/eq_qp.py b/jaxopt/_src/eq_qp.py
index 65fc3936..40fae6b5 100644
--- a/jaxopt/_src/eq_qp.py
+++ b/jaxopt/_src/eq_qp.py
@@ -25,7 +25,7 @@
 
 from jaxopt._src import base
 from jaxopt._src import implicit_diff as idf
-from jaxopt._src.tree_util import tree_add, tree_sub
+from jaxopt._src.tree_util import tree_add, tree_sub, tree_add_scalar_mul
 from jaxopt._src.tree_util import tree_vdot, tree_negative, tree_l2_norm
 from jaxopt._src.linear_operator import _make_linear_operator
 from jaxopt._src.cvxpy_wrapper import _check_params
@@ -143,7 +143,9 @@ def matvec_qp(_, x):
     def matvec_regularized_qp(_, x):
       primal, dual_eq = x
       Stop, Sbottom = matvec(x)
-      return Stop + ridge * primal, Sbottom - ridge * dual_eq
+      a = tree_add_scalar_mul(Stop, ridge, primal)
+      b = tree_add_scalar_mul(Sbottom, -ridge, dual_eq)
+      return a, b
 
     solver = IterativeRefinement(
       matvec_A=matvec_qp,
diff --git a/tests/eq_qp_test.py b/tests/eq_qp_test.py
index 11fb0200..1edc9124 100644
--- a/tests/eq_qp_test.py
+++ b/tests/eq_qp_test.py
@@ -13,6 +13,7 @@
 # limitations under the License.
 
 from absl.testing import absltest
+from absl.testing import parameterized
 
 import jax
 import jax.numpy as jnp
@@ -108,7 +109,9 @@ def test_projection_hyperplane(self):
     self.assertArraysAllClose(primal_sol, expected)
     self.assertAllClose(qp.l2_optimality_error(sol, **hyperparams), 0.0)
 
-  def test_eq_constrained_qp_with_pytrees(self):
+  @parameterized.product(refine_regularization=[0., 1e-6])
+  def test_eq_constrained_qp_with_pytrees(self, refine_regularization):
+    # refine_regularization != 0. triggers a non regression test for issue #311
     rng = onp.random.RandomState(0)
     Q = rng.randn(7, 7)
     Q = onp.dot(Q, Q.T)
@@ -131,7 +134,8 @@ def matvec_A(A, tup):
 
     # With pytrees directly.
     hyperparams = dict(params_obj=(Q, c), params_eq=(A, b))
-    qp = EqualityConstrainedQP(matvec_Q=matvec_Q, matvec_A=matvec_A)
+    qp = EqualityConstrainedQP(matvec_Q=matvec_Q, matvec_A=matvec_A,
+                               refine_regularization=refine_regularization)
     # sol.primal has the same pytree structure as the output of matvec_Q.
     # sol.dual_eq has the same pytree structure as the output of matvec_A.
     sol_pytree = qp.run(**hyperparams).params