# American Institute of Mathematical Sciences

July  2016, 12(3): 1041-1056. doi: 10.3934/jimo.2016.12.1041

## Cardinality constrained portfolio selection problem: A completely positive programming approach

 1 School of Business Administration, Southwestern University of Finance and Economics, Chengdu, 611130 2 Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27606, United States 3 School of Management, University of Chinese Academy of Sciences, Beijing, 100190 4 Department of Management Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310058

Received  March 2014 Revised  May 2015 Published  September 2015

In this paper, we propose a completely positive programming reformulation of the cardinality constrained portfolio selection problem. By constructing a sequence of computable cones of nonnegative quadratic forms over a union of second-order cones, an $\epsilon$-optimal solution of the original problem can be found in finite iterations using semidefinite programming techniques. In order to obtain a good lower bound efficiently, an adaptive scheme is adopted in our approximation algorithm. The numerical results show that the proposed algorithm can find better approximate and feasible solutions than other known methods in the literature.
Citation: Ye Tian, Shucherng Fang, Zhibin Deng, Qingwei Jin. Cardinality constrained portfolio selection problem: A completely positive programming approach. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1041-1056. doi: 10.3934/jimo.2016.12.1041
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##### References:
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