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A Model of Multistage Risk-Averse Stochastic Optimization and its Solution by Scenario-Based Decomposition Algorithms

Author

Listed:
  • Min Zhang

    (State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, P. R. China2University of Chinese Academy of Sciences, Beijing 100049, P. R. China)

  • Liangshao Hou

    (Department of Mathematics, Hong Kong Baptist University, Hong Kong)

  • Jie Sun

    (School of EECMS, Curtin University, Australia and Institute of Mathematics, Hebei University of Technology, P. R. China)

  • Ailing Yan

    (Institute of Mathematics, Hebei University of Technology, P. R. China)

Abstract

Stochastic optimization models based on risk-averse measures are of essential importance in financial management and business operations. This paper studies new algorithms for a popular class of these models, namely, the mean-deviation models in multistage decision making under uncertainty. It is argued that these types of problems enjoy a scenario-decomposable structure, which could be utilized in an efficient progressive hedging procedure. In case that linkage constraints arise in reformulations of the original problem, a Lagrange progressive hedging algorithm could be utilized to solve the reformulated problem. Convergence results of the algorithms are obtained based on the recent development of the Lagrangian form of stochastic variational inequalities. Numerical results are provided to show the effectiveness of the proposed algorithms.

Suggested Citation

  • Min Zhang & Liangshao Hou & Jie Sun & Ailing Yan, 2020. "A Model of Multistage Risk-Averse Stochastic Optimization and its Solution by Scenario-Based Decomposition Algorithms," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(04), pages 1-21, August.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:04:n:s0217595920400047
    DOI: 10.1142/S0217595920400047
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