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Penalty PALM Method for Cardinality Constrained Portfolio Selection Problems

Yue Teng (tengyue86***at***mail.dlut.edu.cn)
Li Yang (yangli96***at***dlut.edu.cn)
Bo Yu (yubo***at***dlut.edu.cn)
Xiaoliang Song (songxiaoliang***at***mail.dlut.edu.cn)

Abstract: 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.

Keywords: Cardinality constrained quadratic programming ; Cardinality constrained portfolio selection ; Proximal alternating linearized minimization method ; Penalty decomposition method ; Sparse projection

Category 1: Applications -- OR and Management Sciences (Finance and Economics )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 07/10/2015
Entry Accepted: 07/10/2015
Entry Last Modified: 11/12/2015

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