  In this paper, we propose a sparse equity portfolio optimization (SEPO) based
on the mean-variance portfolio selection model. Aimed at minimizing transaction
cost by avoiding small investments, this new model includes $\ell_0$-norm
regularization of the asset weights to promote sparsity, hence the acronym
SEPO-$\ell_0$. The selection model is also subjected to a minimum expected
return. The complexity of the model calls for proximal method, which allows us
to handle the objectives terms separately via the corresponding proximal
operators. We develop an efficient ADMM-like algorithm to find the optimal
portfolio and prove its global convergence. The efficiency of the algorithm is
demonstrated using real stock data and the model is promising in portfolio
selection in terms of generating higher expected return while maintaining good
level of sparsity, and thus minimizing transaction cost.
