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

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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.

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Authors and Affiliations

  1. Department of Management Science, School of Management, Fudan University, Shanghai, 200433, People’s Republic of China

    X. T. Cui & X. L. Sun

  2. School of Economics and Management, Tongji University, Shanghai, 200092, People’s Republic of China

    X. J. Zheng

  3. Department of Finance and Investment, Sun Yat-Sen Business School, Sun Yat-Sen University, Guangzhou, 510275, People’s Republic of China

    S. S. Zhu

Authors
  1. X. T. Cui
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  2. X. J. Zheng
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  3. S. S. Zhu
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  4. X. L. Sun
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Corresponding author

Correspondence to X. J. Zheng.

Additional information

This work was supported by National Natural Science Foundation of China under Grants 10971034, 11101092 and 71071036, and by the Joint NSFC/RGC grants under Grant 71061160506.

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Cui, X.T., Zheng, X.J., Zhu, S.S. et al. Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems. J Glob Optim 56, 1409–1423 (2013). https://doi.org/10.1007/s10898-012-9842-2

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  • DOI: https://doi.org/10.1007/s10898-012-9842-2

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