  We consider the l1-regularized Markowitz model, where a l1-penalty term is
added to the objective function of the classical mean-variance one to stabilize
the solution process, promoting sparsity in the solution. The l1-penalty term
can also be interpreted in terms of short sales, on which several financial
markets have posed restrictions. The choice of the regularization parameter
plays a key role to obtain optimal portfolios that meet the financial
requirements. We propose an updating rule for the regularization parameter in
Bregman iteration to control both the sparsity and the number of short
positions. We show that the modified scheme preserves the properties of the
original one. Numerical tests are reported, which show the effectiveness of the
approach.
