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Approximate Methods for Solving Chance-Constrained Linear Programs in Probability Measure Space

Author

Listed:
  • Xun Shen

    (Osaka University)

  • Satoshi Ito

    (The Institute of Statistical Mathematics)

Abstract

A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear program in probability measure space is intractable, and no numerical method exists to solve this problem. This paper presents numerical methods to solve chance-constrained linear programs in probability measure space for the first time. We propose two solvable optimization problems as approximate problems of the original problem. We prove the uniform convergence of each approximate problem. Moreover, numerical experiments have been implemented to validate the proposed methods.

Suggested Citation

  • Xun Shen & Satoshi Ito, 2024. "Approximate Methods for Solving Chance-Constrained Linear Programs in Probability Measure Space," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 150-177, January.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:1:d:10.1007_s10957-023-02342-w
    DOI: 10.1007/s10957-023-02342-w
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    References listed on IDEAS

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    1. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
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    3. Holger Berthold & Holger Heitsch & René Henrion & Jan Schwientek, 2022. "On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 1-37, August.
    4. M. C. Campi & S. Garatti, 2011. "A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 257-280, February.
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