IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v84y2016i1d10.1007_s00186-016-0537-1.html
   My bibliography  Save this article

SAA method based on modified Newton method for stochastic variational inequality with second-order cone constraints and application in portfolio optimization

Author

Listed:
  • Shuang Chen

    (Information and Engineering College of Dalian University)

  • Li-Ping Pang

    (Dalian University of Technology)

  • Xue-Fei Ma

    (Syracuse University)

  • Dan Li

    (Information and Engineering College of Dalian University)

Abstract

In this paper we apply modified Newton method based on sample average approximation (SAA) to solve stochastic variational inequality with stochastic second-order cone constraints (SSOCCVI). Under some moderate conditions, the SAA solution converges to its true counterpart with probability approaching one at exponential rate as sample size increases. We apply the theoretical results for solving a class of stochastic second order cone complementarity problems and stochastic programming problems with stochastic second order cone constraints. Some illustrative examples are given to show how the globally convergent method works and the comparison results between our method and other methods. Furthermore, we apply this method to portfolio optimization with loss risk constraints problems.

Suggested Citation

  • Shuang Chen & Li-Ping Pang & Xue-Fei Ma & Dan Li, 2016. "SAA method based on modified Newton method for stochastic variational inequality with second-order cone constraints and application in portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 129-154, August.
    • Handle: RePEc:spr:mathme:v:84:y:2016:i:1:d:10.1007_s00186-016-0537-1
    DOI: 10.1007/s00186-016-0537-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-016-0537-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-016-0537-1?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. Shaohua Pan & Jein-Shan Chen, 2010. "A semismooth Newton method for SOCCPs based on a one-parametric class of SOC complementarity functions," Computational Optimization and Applications, Springer, vol. 45(1), pages 59-88, January.
    2. Huifu Xu, 2010. "Sample Average Approximation Methods For A Class Of Stochastic Variational Inequality Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 103-119.
    3. F. Maggioni & F. A. Potra & M. I. Bertocchi & E. Allevi, 2009. "Stochastic Second-Order Cone Programming in Mobile Ad Hoc Networks," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 309-328, November.
    4. Jeff Linderoth & Alexander Shapiro & Stephen Wright, 2006. "The empirical behavior of sampling methods for stochastic programming," Annals of Operations Research, Springer, vol. 142(1), pages 215-241, February.
    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. Huifu Xu & Dali Zhang, 2013. "Stochastic Nash equilibrium problems: sample average approximation and applications," Computational Optimization and Applications, Springer, vol. 55(3), pages 597-645, July.
    2. 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.
    3. Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    4. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    5. Xiaotie Chen & David L. Woodruff, 2024. "Distributions and bootstrap for data-based stochastic programming," Computational Management Science, Springer, vol. 21(1), pages 1-21, June.
    6. Shi, Qingxin & Li, Fangxing & Dong, Jin & Olama, Mohammed & Wang, Xiaofei & Winstead, Chris & Kuruganti, Teja, 2022. "Co-optimization of repairs and dynamic network reconfiguration for improved distribution system resilience," Applied Energy, Elsevier, vol. 318(C).
    7. Jörn Dunkel & Stefan Weber, 2010. "Stochastic Root Finding and Efficient Estimation of Convex Risk Measures," Operations Research, INFORMS, vol. 58(5), pages 1505-1521, October.
    8. Soham Ghosh & Sujay Mukhoti, 2023. "Non-parametric generalised newsvendor model," Annals of Operations Research, Springer, vol. 321(1), pages 241-266, February.
    9. Prasad Parab & Lewis Ntaimo & Bernardo Pagnoncelli, 2025. "Stochastic decomposition for risk-averse two-stage stochastic linear programs," Journal of Global Optimization, Springer, vol. 91(1), pages 59-93, January.
    10. Xiao-Juan Zhang & Xue-Wu Du & Zhen-Ping Yang & Gui-Hua Lin, 2019. "An Infeasible Stochastic Approximation and Projection Algorithm for Stochastic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1053-1076, December.
    11. Masato Wada & Felipe Delgado & Bernardo K. Pagnoncelli, 2017. "A risk averse approach to the capacity allocation problem in the airline cargo industry," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(6), pages 643-651, June.
    12. Alzalg, Baha, 2015. "Volumetric barrier decomposition algorithms for stochastic quadratic second-order cone programming," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 494-508.
    13. Aydin, Nezir & Murat, Alper, 2013. "A swarm intelligence based sample average approximation algorithm for the capacitated reliable facility location problem," International Journal of Production Economics, Elsevier, vol. 145(1), pages 173-183.
    14. Salazar, Juan M. & Diwekar, Urmila & Constantinescu, Emil & Zavala, Victor M., 2013. "Stochastic optimization approach to water management in cooling-constrained power plants," Applied Energy, Elsevier, vol. 112(C), pages 12-22.
    15. Ankur Kulkarni & Uday Shanbhag, 2012. "Recourse-based stochastic nonlinear programming: properties and Benders-SQP algorithms," Computational Optimization and Applications, Springer, vol. 51(1), pages 77-123, January.
    16. Xinyu Yao & Karmel S. Shehadeh & Rema Padman, 2024. "Multi-resource allocation and care sequence assignment in patient management: a stochastic programming approach," Health Care Management Science, Springer, vol. 27(3), pages 352-369, September.
    17. Nesbitt, Peter & Blake, Lewis R. & Lamas, Patricio & Goycoolea, Marcos & Pagnoncelli, Bernardo K. & Newman, Alexandra & Brickey, Andrea, 2021. "Underground mine scheduling under uncertainty," European Journal of Operational Research, Elsevier, vol. 294(1), pages 340-352.
    18. Philpott, A.B. & de Matos, V.L., 2012. "Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion," European Journal of Operational Research, Elsevier, vol. 218(2), pages 470-483.
    19. Sanjay Mehrotra & M. Gokhan Ozevin, 2009. "Decomposition Based Interior Point Methods for Two-Stage Stochastic Convex Quadratic Programs with Recourse," Operations Research, INFORMS, vol. 57(4), pages 964-974, August.
    20. Karmel S. Shehadeh & Amy E. M. Cohn & Ruiwei Jiang, 2021. "Using stochastic programming to solve an outpatient appointment scheduling problem with random service and arrival times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(1), pages 89-111, February.

    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:mathme:v:84:y:2016:i:1:d:10.1007_s00186-016-0537-1. 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.