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diff --git a/test/test_optim.py b/test/test_optim.py
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+"""Tests for module optim fro OT optimization """
+
+# Author: Remi Flamary <remi.flamary@unice.fr>
+#
+# License: MIT License
+
+import numpy as np
+import ot
+
+
+def test_conditional_gradient():
+
+    n_bins = 100  # nb bins
+    np.random.seed(0)
+    # bin positions
+    x = np.arange(n_bins, dtype=np.float64)
+
+    # Gaussian distributions
+    a = ot.datasets.make_1D_gauss(n_bins, m=20, s=5)  # m= mean, s= std
+    b = ot.datasets.make_1D_gauss(n_bins, m=60, s=10)
+
+    # loss matrix
+    M = ot.dist(x.reshape((n_bins, 1)), x.reshape((n_bins, 1)))
+    M /= M.max()
+
+    def f(G):
+        return 0.5 * np.sum(G**2)
+
+    def df(G):
+        return G
+
+    reg = 1e-1
+
+    G, log = ot.optim.cg(a, b, M, reg, f, df, verbose=True, log=True)
+
+    np.testing.assert_allclose(a, G.sum(1))
+    np.testing.assert_allclose(b, G.sum(0))
+
+
+def test_generalized_conditional_gradient():
+
+    n_bins = 100  # nb bins
+    np.random.seed(0)
+    # bin positions
+    x = np.arange(n_bins, dtype=np.float64)
+
+    # Gaussian distributions
+    a = ot.datasets.make_1D_gauss(n_bins, m=20, s=5)  # m= mean, s= std
+    b = ot.datasets.make_1D_gauss(n_bins, m=60, s=10)
+
+    # loss matrix
+    M = ot.dist(x.reshape((n_bins, 1)), x.reshape((n_bins, 1)))
+    M /= M.max()
+
+    def f(G):
+        return 0.5 * np.sum(G**2)
+
+    def df(G):
+        return G
+
+    reg1 = 1e-3
+    reg2 = 1e-1
+
+    G, log = ot.optim.gcg(a, b, M, reg1, reg2, f, df, verbose=True, log=True)
+
+    np.testing.assert_allclose(a, G.sum(1), atol=1e-05)
+    np.testing.assert_allclose(b, G.sum(0), atol=1e-05)
+
+
+def test_solve_1d_linesearch_quad_funct():
+    np.testing.assert_allclose(ot.optim.solve_1d_linesearch_quad(1, -1, 0), 0.5)
+    np.testing.assert_allclose(ot.optim.solve_1d_linesearch_quad(-1, 5, 0), 0)
+    np.testing.assert_allclose(ot.optim.solve_1d_linesearch_quad(-1, 0.5, 0), 1)