For reducing costs of market frictions, investors need to build a small-scale portfolio by solving a cardinality constrained portfolio selection problem which is NP-hard in general and not easy to be solved eciently for a large-scale problem. In this paper, we propose a penalty proximal alternat- ing linearized minimization method for the large-scale problems in which a sequence of penalty subproblems are solved by utilizing proximal alternating linearized minimization frame and sparse projection techniques. For exploit- ing the structure of the problems and reducing the computation complexity, each penalty subproblem is solved by alternately solving two projection sub- problems. The global convergence of the method to a KKT point or a local minimizer of the problem can be proved under the characteristic of the prob- lem. The computational results with practical problems demonstrate that our method can nd the suboptimal solutions of the problems eciently and is competitive with some other local solution methods.
View Penalty PALM Method for Cardinality Constrained Portfolio Selection Problems