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New reformulations for probabilistically constrained quadratic programs

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  • Hsia, Yong
  • Wu, Baiyi
  • Li, Duan

Abstract

The mixed integer quadratic programming (MIQP) reformulation by Zheng, Sun, Li, and Cui (2012) for probabilistically constrained quadratic programs (PCQP) recently published in EJOR significantly dominates the standard MIQP formulation (Ruszczynski, 2002; Benati & Rizzi, 2007) which has been widely adopted in the literature. Stimulated by the dimensionality problem which Zheng et al. (2012) acknowledge themselves for their reformulations, we study further the characteristics of PCQP and develop new MIQP reformulations for PCQP with fewer variables and constraints. The results from numerical tests demonstrate that our reformulations clearly outperform the state-of-the-art MIQP in Zheng et al. (2012).

Suggested Citation

  • Hsia, Yong & Wu, Baiyi & Li, Duan, 2014. "New reformulations for probabilistically constrained quadratic programs," European Journal of Operational Research, Elsevier, vol. 233(3), pages 550-556.
    • Handle: RePEc:eee:ejores:v:233:y:2014:i:3:p:550-556
    DOI: 10.1016/j.ejor.2013.08.052
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    References listed on IDEAS

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    1. Zheng, Xiaojin & Sun, Xiaoling & Li, Duan & Cui, Xueting, 2012. "Lagrangian decomposition and mixed-integer quadratic programming reformulations for probabilistically constrained quadratic programs," European Journal of Operational Research, Elsevier, vol. 221(1), pages 38-48.
    2. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    3. Miguel A. Lejeune, 2012. "Pattern-Based Modeling and Solution of Probabilistically Constrained Optimization Problems," Operations Research, INFORMS, vol. 60(6), pages 1356-1372, December.
    4. Benati, Stefano & Rizzi, Romeo, 2007. "A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 423-434, January.
    5. Darinka Dentcheva & Gabriela Martinez, 2012. "Augmented Lagrangian method for probabilistic optimization," Annals of Operations Research, Springer, vol. 200(1), pages 109-130, November.
    6. Pierre Bonami & Miguel A. Lejeune, 2009. "An Exact Solution Approach for Integer Constrained Portfolio Optimization Problems Under Stochastic Constraints," Post-Print hal-00421756, HAL.
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    Cited by:

    1. Ran Ji & Miguel A. Lejeune, 2018. "Risk-budgeting multi-portfolio optimization with portfolio and marginal risk constraints," Annals of Operations Research, Springer, vol. 262(2), pages 547-578, March.
    2. Wu, Baiyi & Li, Duan & Jiang, Rujun, 2019. "Quadratic convex reformulation for quadratic programming with linear on–off constraints," European Journal of Operational Research, Elsevier, vol. 274(3), pages 824-836.

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