diff --git a/ot/optim.py b/ot/optim.py
index c4198a00a..8700f75d1 100644
--- a/ot/optim.py
+++ b/ot/optim.py
@@ -297,7 +297,7 @@ def cost(G):
             loop = 0
 
         abs_delta_cost_G = abs(cost_G - old_cost_G)
-        relative_delta_cost_G = abs_delta_cost_G / abs(cost_G)
+        relative_delta_cost_G = abs_delta_cost_G / abs(cost_G) if cost_G != 0. else np.nan
         if relative_delta_cost_G < stopThr or abs_delta_cost_G < stopThr2:
             loop = 0
 
diff --git a/test/test_gromov.py b/test/test_gromov.py
index 559d07855..846e69f2b 100644
--- a/test/test_gromov.py
+++ b/test/test_gromov.py
@@ -8,10 +8,12 @@
 # License: MIT License
 
 import numpy as np
+import pytest
+import warnings
+
 import ot
 from ot.backend import NumpyBackend
 from ot.backend import torch, tf
-import pytest
 
 
 def test_gromov(nx):
@@ -146,8 +148,10 @@ def test_gromov_dtype_device(nx):
 
         C1b, C2b, pb, qb, G0b = nx.from_numpy(C1, C2, p, q, G0, type_as=tp)
 
-        Gb = ot.gromov.gromov_wasserstein(C1b, C2b, pb, qb, 'square_loss', G0=G0b, verbose=True)
-        gw_valb = ot.gromov.gromov_wasserstein2(C1b, C2b, pb, qb, 'kl_loss', armijo=True, G0=G0b, log=False)
+        with warnings.catch_warnings():
+            warnings.filterwarnings('error')
+            Gb = ot.gromov.gromov_wasserstein(C1b, C2b, pb, qb, 'square_loss', G0=G0b, verbose=True)
+            gw_valb = ot.gromov.gromov_wasserstein2(C1b, C2b, pb, qb, 'kl_loss', armijo=True, G0=G0b, log=False)
 
         nx.assert_same_dtype_device(C1b, Gb)
         nx.assert_same_dtype_device(C1b, gw_valb)