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Risk-Averse Optimal Control Model Under Uncertainty and Its Modified Progressive Hedging Algorithm

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  • Jie Sun

    (Curtin University)

  • Di Wu

    (Shanghai University of Engineering Science)

  • Changjun Yu

    (Shanghai University)

Abstract

It is of practical importance to incorporate a risk-averse objective in an optimal control problem under uncertainty. By leveraging the dual relationship between risk and regret measures, the risk-averse optimal control problem can be equivalently transformed into an optimal control problem with nonanticipativity constraints and expectation objective function. A modified progressive hedging algorithm is then proposed to solve the transformed problem, in which the descent conditions are enforced to ensure global convergence of the algorithm. Numerical results of three different types of problems are presented to show the applicability and effectiveness of the modified progressive hedging algorithm.

Suggested Citation

  • Jie Sun & Di Wu & Changjun Yu, 2024. "Risk-Averse Optimal Control Model Under Uncertainty and Its Modified Progressive Hedging Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 960-984, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02540-0
    DOI: 10.1007/s10957-024-02540-0
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    References listed on IDEAS

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    1. Ang, James & Meng, Fanwen & Sun, Jie, 2014. "Two-stage stochastic linear programs with incomplete information on uncertainty," European Journal of Operational Research, Elsevier, vol. 233(1), pages 16-22.
    2. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    3. 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.
    4. Jie Sun & Xinmin Yang & Qiang Yao & Min Zhang, 2017. "Risk Minimization, Regret Minimization and Progressive Hedging Algorithms," Papers 1705.00340, arXiv.org, revised Jun 2020.
    5. Marcus Ang & Jie Sun & Qiang Yao, 2018. "On the dual representation of coherent risk measures," Annals of Operations Research, Springer, vol. 262(1), pages 29-46, March.
    6. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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