Sparsity penalized mean-variance portfolio selection: analysis and computation

We consider the problem of mean-variance portfolio selection regularized with an & $\ell _0$-penalty term to control the sparsity of the portfolio. We analyze the structure of local and global minimizers and use our results in the design of a Branch-and-Bound algorithm coupled with an advanced start heuristic. Extensive computational results with real data as well as comparisons with an off-the-shelf and state-of-the-art (MIQP) solver are reported.