Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems

Authors:
X. T. Cui;X. J. Zheng;S. S. Zhu;X. L. Sun
Affiliations:
Department of Management Science, School of Management, Fudan University, Shanghai, People's Republic of China 200433;School of Economics and Management, Tongji University, Shanghai, People's Republic of China 200092;Department of Finance and Investment, Sun Yat-Sen Business School, Sun Yat-Sen University, Guangzhou, People's Republic of China 510275;Department of Management Science, School of Management, Fudan University, Shanghai, People's Republic of China 200433
Venue:
Journal of Global Optimization
Year:
2013

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Abstract

In this paper we investigate a class of cardinality-constrained portfolio selection problems. We construct convex relaxations for this class of optimization problems via a new Lagrangian decomposition scheme. We show that the dual problem can be reduced to a second-order cone program problem which is tighter than the continuous relaxation of the standard mixed integer quadratically constrained quadratic program (MIQCQP) reformulation. We then propose a new MIQCQP reformulation which is more efficient than the standard MIQCQP reformulation in terms of the tightness of the continuous relaxations. Computational results are reported to demonstrate the tightness of the SOCP relaxation and the effectiveness of the new MIQCQP reformulation.