def _f_j(q_j, b_j_norm, a_1_j, a_2_j, m):
    """Compute the objective with respect to one of the coefficients i.e.
    (1/2m)||q_j||^2 + a_1||b_j|| + (a_2/2)||b_j||^2.
    """
    return (
        ((q_j @ q_j) / (2.0 * m))
        + (a_1_j * b_j_norm)
        + ((a_2_j / 2.0) * (b_j_norm ** 2))
    )