IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v58y2014i2p483-501.html
   My bibliography  Save this article

CVaR-constrained stochastic programming reformulation for stochastic nonlinear complementarity problems

Author

Listed:
  • Liyan Xu
  • Bo Yu

Abstract

We reformulate a stochastic nonlinear complementarity problem as a stochastic programming problem which minimizes an expected residual defined by a restricted NCP function with nonnegative constraints and CVaR constraints which guarantee the stochastic nonlinear function being nonnegative with a high probability. By applying smoothing technique and penalty method, we propose a penalized smoothing sample average approximation algorithm to solve the CVaR-constrained stochastic programming. We show that the optimal solution of the penalized smoothing sample average approximation problem converges to the solution of the corresponding nonsmooth CVaR-constrained stochastic programming problem almost surely. Finally, we report some preliminary numerical test results. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Liyan Xu & Bo Yu, 2014. "CVaR-constrained stochastic programming reformulation for stochastic nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 58(2), pages 483-501, June.
    • Handle: RePEc:spr:coopap:v:58:y:2014:i:2:p:483-501
    DOI: 10.1007/s10589-013-9625-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-013-9625-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-013-9625-9?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. Xiaojun Chen & Masao Fukushima, 2005. "Expected Residual Minimization Method for Stochastic Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1022-1038, November.
    2. M. Wang & M. M. Ali, 2010. "Stochastic Nonlinear Complementarity Problems: Stochastic Programming Reformulation and Penalty-Based Approximation Method," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 597-614, March.
    3. N. Yamashita, 1998. "Properties of Restricted NCP Functions for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 701-717, September.
    4. C. Zhang & X. Chen, 2008. "Stochastic Nonlinear Complementarity Problem and Applications to Traffic Equilibrium under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 277-295, May.
    5. G. L. Zhou & L. Caccetta, 2008. "Feasible Semismooth Newton Method for a Class of Stochastic Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 379-392, November.
    6. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    7. Kenji Hamatani & Masao Fukushima, 2011. "Pricing American options with uncertain volatility through stochastic linear complementarity models," Computational Optimization and Applications, Springer, vol. 50(2), pages 263-286, October.
    Full references (including those not matched with items on IDEAS)

    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. M. J. Luo & G. H. Lin, 2009. "Expected Residual Minimization Method for Stochastic Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 103-116, January.
    2. Fang Lu & Shengjie Li & Jing Yang, 2015. "Convergence analysis of weighted expected residual method for nonlinear stochastic variational inequality problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 229-242, October.
    3. M. J. Luo & G. H. Lin, 2009. "Convergence Results of the ERM Method for Nonlinear Stochastic Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 569-581, September.
    4. Shouqiang Du & Liyuan Cui & Yuanyuan Chen & Yimin Wei, 2022. "Stochastic Tensor Complementarity Problem with Discrete Distribution," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 912-929, March.
    5. Yakui Huang & Hongwei Liu, 2016. "Smoothing projected Barzilai–Borwein method for constrained non-Lipschitz optimization," Computational Optimization and Applications, Springer, vol. 65(3), pages 671-698, December.
    6. Johanna Burtscheidt & Matthias Claus, 2017. "A Note on Stability for Risk-Averse Stochastic Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 298-308, January.
    7. Zhang, Chao & Chen, Xiaojun & Sumalee, Agachai, 2011. "Robust Wardrop's user equilibrium assignment under stochastic demand and supply: Expected residual minimization approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 534-552, March.
    8. Wang, Guoxin & Zhang, Jin & Zeng, Bo & Lin, Gui-Hua, 2018. "Expected residual minimization formulation for a class of stochastic linear second-order cone complementarity problems," European Journal of Operational Research, Elsevier, vol. 265(2), pages 437-447.
    9. Min Li & Chao Zhang, 2020. "Two-Stage Stochastic Variational Inequality Arising from Stochastic Programming," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 324-343, July.
    10. Lu, Fang & Li, Sheng-jie, 2015. "Method of weighted expected residual for solving stochastic variational inequality problems," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 651-663.
    11. M. Wang & M. M. Ali, 2010. "Stochastic Nonlinear Complementarity Problems: Stochastic Programming Reformulation and Penalty-Based Approximation Method," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 597-614, March.
    12. Ming-Zheng Wang & M. Ali, 2014. "On the ERM formulation and a stochastic approximation algorithm of the stochastic- $$R_0$$ R 0 EVLCP," Annals of Operations Research, Springer, vol. 217(1), pages 513-534, June.
    13. Sofiane Aboura, 2014. "When the U.S. Stock Market Becomes Extreme?," Risks, MDPI, vol. 2(2), pages 1-15, May.
    14. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
    15. Christina Büsing & Sigrid Knust & Xuan Thanh Le, 2018. "Trade-off between robustness and cost for a storage loading problem: rule-based scenario generation," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 339-365, December.
    16. Winter, Peter, 2007. "Managerial Risk Accounting and Control – A German perspective," MPRA Paper 8185, University Library of Munich, Germany.
    17. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    18. Jiang Cheng & Hung-Gay Fung & Tzu-Ting Lin & Min-Ming Wen, 2024. "CEO optimism and the use of credit default swaps: evidence from the US life insurance industry," Review of Quantitative Finance and Accounting, Springer, vol. 63(1), pages 169-194, July.
    19. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2014. "Beyond cash-additive risk measures: when changing the numéraire fails," Finance and Stochastics, Springer, vol. 18(1), pages 145-173, January.
    20. Li, Xiao-Ming & Rose, Lawrence C., 2009. "The tail risk of emerging stock markets," Emerging Markets Review, Elsevier, vol. 10(4), pages 242-256, December.

    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:spr:coopap:v:58:y:2014:i:2:p:483-501. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.