Before revision:  However, efforts to translate this theoretical foundation into a viable portfolio construction algorithm have been plagued by technical difficulties stemming from the instability of the original optimization problemwith respect to the available data. In this paper we address these issues of estimation error by regularizing the Markowitz objective function through the addition of an \ell_1 penalty  .
After revision:  To stabilize the problem, we propose to add to the Markowitz objective function through the addition of an \ell_1 penalty .