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Robust approximation of chance constrained optimization with polynomial perturbation

Author

Listed:
  • Bo Rao

    (Xiangtan University)

  • Liu Yang

    (Xiangtan University
    Xiangtan University)

  • Suhan Zhong

    (Texas A&M University)

  • Guangming Zhou

    (Xiangtan University
    Xiangtan University)

Abstract

This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a robust approximation by replacing the chance constraint with a robust constraint over an uncertainty set. When the objective function is linear or SOS-convex, the robust approximation can be equivalently transformed into linear conic optimization. Semidefinite relaxation algorithms are proposed to solve these linear conic transformations globally and their convergent properties are studied. We also introduce a heuristic method to find efficient uncertainty sets such that optimizers of the robust approximation are feasible to the original problem. Numerical experiments are given to show the efficiency of our method.

Suggested Citation

  • Bo Rao & Liu Yang & Suhan Zhong & Guangming Zhou, 2024. "Robust approximation of chance constrained optimization with polynomial perturbation," Computational Optimization and Applications, Springer, vol. 89(3), pages 977-1003, December.
    • Handle: RePEc:spr:coopap:v:89:y:2024:i:3:d:10.1007_s10589-024-00602-7
    DOI: 10.1007/s10589-024-00602-7
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    References listed on IDEAS

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    1. Yuan Yuan & Zukui Li & Biao Huang, 2017. "Robust optimization approximation for joint chance constrained optimization problem," Journal of Global Optimization, Springer, vol. 67(4), pages 805-827, April.
    2. L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
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    Full references (including those not matched with items on IDEAS)

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