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

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  • X. Cui
  • X. Zheng
  • S. Zhu
  • X. Sun

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. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • X. Cui & X. Zheng & S. Zhu & X. Sun, 2013. "Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1409-1423, August.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:4:p:1409-1423
    DOI: 10.1007/s10898-012-9842-2
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    References listed on IDEAS

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    Cited by:

    1. Janusz Miroforidis, 2021. "Bounds on efficient outcomes for large-scale cardinality-constrained Markowitz problems," Journal of Global Optimization, Springer, vol. 80(3), pages 617-634, July.
    2. Xiaojin Zheng & Yutong Pan & Xueting Cui, 2018. "Quadratic convex reformulation for nonconvex binary quadratically constrained quadratic programming via surrogate constraint," Journal of Global Optimization, Springer, vol. 70(4), pages 719-735, April.
    3. Jize Zhang & Tim Leung & Aleksandr Aravkin, 2018. "A Relaxed Optimization Approach for Cardinality-Constrained Portfolio Optimization," Papers 1810.10563, arXiv.org.
    4. Zhi-Long Dong & Fengmin Xu & Yu-Hong Dai, 2020. "Fast algorithms for sparse portfolio selection considering industries and investment styles," Journal of Global Optimization, Springer, vol. 78(4), pages 763-789, December.
    5. Xiaojin Zheng & Yutong Pan & Zhaolin Hu, 2021. "Perspective Reformulations of Semicontinuous Quadratically Constrained Quadratic Programs," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 163-179, January.
    6. Carina Moreira Costa & Dennis Kreber & Martin Schmidt, 2022. "An Alternating Method for Cardinality-Constrained Optimization: A Computational Study for the Best Subset Selection and Sparse Portfolio Problems," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 2968-2988, November.
    7. Xiaojin Zheng & Xiaoling Sun & Duan Li, 2014. "Improving the Performance of MIQP Solvers for Quadratic Programs with Cardinality and Minimum Threshold Constraints: A Semidefinite Program Approach," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 690-703, November.
    8. Xingmei Li & Yaxian Wang & Qingyou Yan & Xinchao Zhao, 2019. "Uncertain mean-variance model for dynamic project portfolio selection problem with divisibility," Fuzzy Optimization and Decision Making, Springer, vol. 18(1), pages 37-56, March.
    9. Antonio Frangioni & Claudio Gentile & James Hungerford, 2020. "Decompositions of Semidefinite Matrices and the Perspective Reformulation of Nonseparable Quadratic Programs," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 15-33, February.
    10. Ye Tian & Miao Sun & Zuoliang Ye & Wei Yang, 2016. "Expanded models of the project portfolio selection problem with loss in divisibility," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(8), pages 1097-1107, August.
    11. Wei Xu & Jie Tang & Ka Fai Cedric Yiu & Jian Wen Peng, 2024. "An Efficient Global Optimal Method for Cardinality Constrained Portfolio Optimization," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 690-704, March.
    12. Rujun Jiang & Duan Li, 2019. "Second order cone constrained convex relaxations for nonconvex quadratically constrained quadratic programming," Journal of Global Optimization, Springer, vol. 75(2), pages 461-494, October.
    13. Dimitris Bertsimas & Ryan Cory-Wright, 2022. "A Scalable Algorithm for Sparse Portfolio Selection," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1489-1511, May.

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