diff --git a/tests/optimizers/test_optimizers.py b/tests/optimizers/test_optimizers.py
index a7549842f..8c8f27b03 100644
--- a/tests/optimizers/test_optimizers.py
+++ b/tests/optimizers/test_optimizers.py
@@ -1,4 +1,5 @@
 """Test optimizers."""
+
 import functools
 
 import chex
@@ -17,6 +18,7 @@
     lbfgs_inverse_hessian_formula_2,
     lbfgs_recover_alpha,
     minimize_lbfgs,
+    optax_lbfgs,
 )
 
 
@@ -154,5 +156,59 @@ def loss_fn(x):
         np.testing.assert_allclose(inv_hess_1, inv_hess_2, rtol=0.01)
 
 
+class TestOptaxLBFGS(chex.TestCase):
+    def test_optax_lbfgs(
+        self,
+        maxcor=6,
+        maxiter=1000,
+        ftol=1e-5,
+        gtol=1e-8,
+        maxls=1000,
+    ):
+        """Test the optax_lbfgs function for consistency in history and convergence."""
+
+        def example_fun(w):
+            return jnp.sum(100.0 * (w[1:] - w[:-1] ** 2) ** 2 + (1.0 - w[:-1]) ** 2)
+
+        x0_example = jnp.zeros((8,))
+
+        (final_params, final_state), history = optax_lbfgs(
+            example_fun,
+            x0_example,
+            maxcor=maxcor,
+            maxiter=maxiter,
+            ftol=ftol,
+            gtol=gtol,
+            maxls=maxls,
+        )
+
+        # test that the history is correct
+        L = history.iter.shape[0]
+
+        for l in range(1, L):
+            last = history.last[l]
+            current_s = history.s[l]
+            sml = jnp.delete(current_s, last, axis=0)
+
+            previous_s = history.s[l - 1]
+            previous_sml = jnp.delete(previous_s, last, axis=0)
+
+            np.testing.assert_allclose(
+                previous_sml,
+                sml,
+                err_msg=f"l = {l}, last = {last}, previous_sml = {previous_sml}, sml = {sml}",
+            )
+
+        # additional checks for convergence
+        expected_solution = jnp.ones((8,))
+        np.testing.assert_allclose(
+            final_params,
+            expected_solution,
+            rtol=1e-2,
+            err_msg="Final parameters did not converge to expected solution.",
+        )
+
+
 if __name__ == "__main__":
-    absltest.main()
+    # absltest.main()
+    TestOptaxLBFGS().test_optax_lbfgs()