def par_y0bstep(i):
    r"""The parallel component of the step to minimise the augmented
    Lagrangian with respect to :math:`\mathbf{y}_0`.

    Parameters
    ----------
    i : int
      Index of grouping to update
    """

    global mp_Y0
    mp_Y0[i] = 1/mp_rho*mp_S + mp_DX[i] + mp_U0[i] + mp_b
r"""The parallel component of the step to minimise the augmented
    Lagrangian with respect to :math:`\mathbf{y}_0`.

    Parameters
    ----------
    i : int
      Index of grouping to update