diff --git a/docs/quadratic_programming.rst b/docs/quadratic_programming.rst
index 30009e84..ce938d7d 100644
--- a/docs/quadratic_programming.rst
+++ b/docs/quadratic_programming.rst
@@ -195,6 +195,9 @@ Example::
 
 It is also possible to specify only equality constraints or only inequality
 constraints by setting ``params_eq`` or ``params_ineq`` to ``None``.
+Use ``None`` for a missing constraint family rather than empty arrays, such as
+zero-row equality matrices. If both equality and inequality constraints are
+absent, use the unconstrained QP approach below instead of :class:`jaxopt.OSQP`.
 
 OSQP
 ~~~~
@@ -231,6 +234,12 @@ Example::
 
 See :class:`jaxopt.BoxOSQP` for a full description of the parameters.
 
+When using :class:`jaxopt.OSQP`, pass ``params_eq=None`` if there are no
+equality constraints, or ``params_ineq=None`` if there are no inequality
+constraints. At least one of these two arguments must be provided. Problems
+without constraints should be solved as unconstrained QPs, for example with
+conjugate gradient.
+
 .. topic:: Example
 
    * :ref:`sphx_glr_auto_examples_constrained_multiclass_linear_svm.py`
diff --git a/jaxopt/_src/osqp.py b/jaxopt/_src/osqp.py
index 83cb920f..bd8fe5d8 100644
--- a/jaxopt/_src/osqp.py
+++ b/jaxopt/_src/osqp.py
@@ -1058,8 +1058,12 @@ def run(self,
         a tuple (Q, c) with Q a pytree of matrices,
         or a tuple (params_Q, c) if ``matvec_Q`` is provided,
         or an arbitrary pytree if ``fun`` is provided.
-      params_eq: (A, b) or None if no equality constraints.
-      params_ineq: (G, h) or None if no inequality constraints.
+      params_eq: (A, b) or None if no equality constraints. Use None rather
+        than an empty equality matrix.
+      params_ineq: (G, h) or None if no inequality constraints. Use None
+        rather than an empty inequality matrix. At least one of params_eq or
+        params_ineq must be not None; use an unconstrained QP solver when both
+        constraint families are absent.
     Returns:
       (params, state), ``params = (primal_var, dual_var_eq, dual_var_ineq)``
     """