IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v233y2014i3p550-556.html
   My bibliography  Save this article

New reformulations for probabilistically constrained quadratic programs

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713007364
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.08.052?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Pierre Bonami & Miguel A. Lejeune, 2009. "An Exact Solution Approach for Integer Constrained Portfolio Optimization Problems Under Stochastic Constraints," Post-Print hal-00421756, HAL.
    3. Darinka Dentcheva & Gabriela Martinez, 2012. "Augmented Lagrangian method for probabilistic optimization," Annals of Operations Research, Springer, vol. 200(1), pages 109-130, November.
    4. 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.
    5. Miguel A. Lejeune, 2012. "Pattern-Based Modeling and Solution of Probabilistically Constrained Optimization Problems," Operations Research, INFORMS, vol. 60(6), pages 1356-1372, December.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Xiaodi Bai & Jie Sun & Xiaojin Zheng, 2021. "An Augmented Lagrangian Decomposition Method for Chance-Constrained Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1056-1069, July.
    3. Xueting Cui & Xiaoling Sun & Shushang Zhu & Rujun Jiang & Duan Li, 2018. "Portfolio Optimization with Nonparametric Value at Risk: A Block Coordinate Descent Method," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 454-471, August.
    4. 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.
    5. Miguel A. Lejeune & François Margot, 2016. "Solving Chance-Constrained Optimization Problems with Stochastic Quadratic Inequalities," Operations Research, INFORMS, vol. 64(4), pages 939-957, August.
    6. 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.
    7. Ran Ji & Miguel A. Lejeune, 2021. "Data-Driven Optimization of Reward-Risk Ratio Measures," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1120-1137, July.
    8. Murray, Chase C. & Talukdar, Debabrata & Gosavi, Abhijit, 2010. "Joint Optimization of Product Price, Display Orientation and Shelf-Space Allocation in Retail Category Management," Journal of Retailing, Elsevier, vol. 86(2), pages 125-136.
    9. Zhi-Hai Zhang & Kang Li, 2015. "A novel probabilistic formulation for locating and sizing emergency medical service stations," Annals of Operations Research, Springer, vol. 229(1), pages 813-835, June.
    10. Lukáš Adam & Martin Branda, 2016. "Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 419-436, August.
    11. Martin Branda & Max Bucher & Michal Červinka & Alexandra Schwartz, 2018. "Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization," Computational Optimization and Applications, Springer, vol. 70(2), pages 503-530, June.
    12. Zhang, Zhi-Hai & Unnikrishnan, Avinash, 2016. "A coordinated location-inventory problem in closed-loop supply chain," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 127-148.
    13. Eduardo Bered Fernandes Vieira & Tiago Pascoal Filomena, 2020. "Liquidity Constraints for Portfolio Selection Based on Financial Volume," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 1055-1077, December.
    14. Massol, Olivier & Banal-Estañol, Albert, 2014. "Export diversification through resource-based industrialization: The case of natural gas," European Journal of Operational Research, Elsevier, vol. 237(3), pages 1067-1082.
    15. Moarefdoost, M. Mohsen & Lamadrid, Alberto J. & Zuluaga, Luis F., 2016. "A robust model for the ramp-constrained economic dispatch problem with uncertain renewable energy," Energy Economics, Elsevier, vol. 56(C), pages 310-325.
    16. Liu, Kanglin & Zhang, Zhi-Hai, 2018. "Capacitated disassembly scheduling under stochastic yield and demand," European Journal of Operational Research, Elsevier, vol. 269(1), pages 244-257.
    17. Chien-Ming Chen & Joe Zhu, 2011. "Efficient Resource Allocation via Efficiency Bootstraps: An Application to R&D Project Budgeting," Operations Research, INFORMS, vol. 59(3), pages 729-741, June.
    18. Xiaojin Zheng & Xiaoling Sun & Duan Li & Jie Sun, 2014. "Successive convex approximations to cardinality-constrained convex programs: a piecewise-linear DC approach," Computational Optimization and Applications, Springer, vol. 59(1), pages 379-397, October.
    19. Philipp Baumann & Norbert Trautmann, 2013. "Portfolio-optimization models for small investors," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 345-356, June.
    20. Tiago P. Filomena & Miguel A. Lejeune, 2014. "Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 308-329, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:233:y:2014:i:3:p:550-556. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.