Before revision:  The no-short selling constraint acts as an asymmetric \ell_1 regularizer, setting some  portfolio weights to zero and keeping the estimation error bounded, avoiding the divergence present in the non-regularized case.
After revision:  The no-short selling constraint acts as an asymmetric \ell_1 regularizer, setting some portfolio weights to zero and keeping the out of sample estimator for the variance bounded, avoiding the divergence present in the non-regularized case.