Fix sign error with log_sum_exp (#1689)

* fix sign error with log_sum_exp

* docs

(cherry picked from commit 06854d9)

cvxpy/atoms/log_sum_exp.py

@@ -69,7 +69,8 @@ def _column_grad(self, value):
     def sign_from_args(self) -> Tuple[bool, bool]:
         """Returns sign (is positive, is negative) of the expression.
         """
-        return (False, False)
+        # Non-negative when arg is non-negative.
+        return (self.args[0].is_nonneg(), False)
 
     def is_atom_convex(self) -> bool:
         """Is the atom convex?

cvxpy/tests/test_atoms.py

@@ -1167,3 +1167,18 @@ def test_loggamma(self) -> None:
                           [X == A])
         result = prob.solve(solver=cp.SCS)
         assert np.isclose(result, true_val.sum(), atol=1e0)
+
+    def test_log_sum_exp(self) -> None:
+        """Test log_sum_exp sign.
+        """
+        # Test for non-negative x
+        x = Variable(nonneg=True)
+        atom = cp.log_sum_exp(x)
+        self.assertEqual(atom.curvature, s.CONVEX)
+        self.assertEqual(atom.sign, s.NONNEG)
+
+        # Test for non-positive x
+        x = Variable(nonpos=True)
+        atom = cp.log_sum_exp(x)
+        self.assertEqual(atom.curvature, s.CONVEX)
+        self.assertEqual(atom.sign, s.UNKNOWN)