def EuclidianPO(x, k, norm_X):
    """ Proximal operator for Euclidian norm. It returns:
            prox_k(x) = (1 - k/max(k, \|X\|_2))x
    """
    if norm_X<=k:
        out = 0.0
    else:
        out = (1 - k/norm_X) * x
    return out