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

Author

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  • 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
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    References listed on IDEAS

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    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.
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