diff --git a/docs/changelog.rst b/docs/changelog.rst
index 516fec9e..f245e0fe 100644
--- a/docs/changelog.rst
+++ b/docs/changelog.rst
@@ -1,6 +1,20 @@
 Changelog
 =========
 
+Version 0.4.2
+-------------
+
+Bug fixes and enhancements
+~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+- Fix issue with positional arguments in :class:`jaxopt.LBFGS` and :class:`jaxopt.NonlinearCG`,
+  by Mathieu Blondel.
+
+Contributors
+~~~~~~~~~~~~
+
+Mathieu Blondel.
+
 Version 0.4.1
 -------------
 
diff --git a/jaxopt/_src/lbfgs.py b/jaxopt/_src/lbfgs.py
index 301d7cf9..b34339a7 100644
--- a/jaxopt/_src/lbfgs.py
+++ b/jaxopt/_src/lbfgs.py
@@ -280,9 +280,9 @@ def update(self,
                                 self.max_stepsize,
                                 # Otherwise, we increase a bit the previous one.
                                 state.stepsize * self.increase_factor)
-      new_stepsize, ls_state = ls.run(init_stepsize=init_stepsize,
-                                      params=params, value=value, grad=grad,
-                                      descent_direction=descent_direction,
+      new_stepsize, ls_state = ls.run(init_stepsize,
+                                      params, value, grad,
+                                      descent_direction,
                                       *args, **kwargs)
       new_value = ls_state.value
       new_params = ls_state.params
diff --git a/jaxopt/_src/nonlinear_cg.py b/jaxopt/_src/nonlinear_cg.py
index 15e63668..88603f41 100644
--- a/jaxopt/_src/nonlinear_cg.py
+++ b/jaxopt/_src/nonlinear_cg.py
@@ -139,10 +139,11 @@ def update(self,
                                 maxiter=self.maxls,
                                 decrease_factor=self.decrease_factor,
                                 condition=self.condition)
-    new_stepsize, ls_state = ls.run(init_stepsize=init_stepsize,
-                                    params=params,
-                                    value=value,
-                                    grad=grad,
+    new_stepsize, ls_state = ls.run(init_stepsize,
+                                    params,
+                                    value,
+                                    grad,
+                                    None, # descent_direction
                                     *args, **kwargs)
 
     new_params = tree_add_scalar_mul(params, new_stepsize, descent_direction)
diff --git a/jaxopt/version.py b/jaxopt/version.py
index c9cfab72..e0b5b397 100644
--- a/jaxopt/version.py
+++ b/jaxopt/version.py
@@ -14,4 +14,4 @@
 
 """JAXopt version."""
 
-__version__ = "0.4.1"
+__version__ = "0.4.2"
diff --git a/tests/lbfgs_test.py b/tests/lbfgs_test.py
index 0d64a2d2..55ee85a4 100644
--- a/tests/lbfgs_test.py
+++ b/tests/lbfgs_test.py
@@ -213,6 +213,7 @@ def test_binary_logreg(self, use_gamma):
 
     w_init = jnp.zeros(X.shape[1])
     lbfgs = LBFGS(fun=fun, tol=1e-3, maxiter=500, use_gamma=use_gamma)
+    # Test with keyword argument.
     w_fit, info = lbfgs.run(w_init, data=data)
 
     # Check optimality conditions.
@@ -236,7 +237,8 @@ def test_multiclass_logreg(self, use_gamma):
     pytree_init = (W_init, b_init)
 
     lbfgs = LBFGS(fun=fun, tol=1e-3, maxiter=500, use_gamma=use_gamma)
-    pytree_fit, info = lbfgs.run(pytree_init, data=data)
+    # Test with positional argument.
+    pytree_fit, info = lbfgs.run(pytree_init, data)
 
     # Check optimality conditions.
     self.assertLessEqual(info.error, 1e-2)
diff --git a/tests/nonlinear_cg_test.py b/tests/nonlinear_cg_test.py
index adf02c0b..84bbe2e6 100644
--- a/tests/nonlinear_cg_test.py
+++ b/tests/nonlinear_cg_test.py
@@ -81,7 +81,8 @@ def test_binary_logreg(self, method):
 
     w_init = jnp.zeros(X.shape[1])
     cg_model = NonlinearCG(fun=fun, tol=1e-3, maxiter=100, method=method)
-    w_fit, info = cg_model.run(w_init, data=data)
+    # Test with positional argument.
+    w_fit, info = cg_model.run(w_init, data)
 
     # Check optimality conditions.
     self.assertLessEqual(info.error, 5e-2)