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Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach

Author

Listed:
  • L. Jeff Hong

    (Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

  • Yi Yang

    (Department of Computer Science, University of California, Irvine, Irvine, California 92617)

  • Liwei Zhang

    (School of Mathematical Science, Dalian University of Technology, Dalian 116024, China)

Abstract

When there is parameter uncertainty in the constraints of a convex optimization problem, it is natural to formulate the problem as a joint chance constrained program (JCCP), which requires that all constraints be satisfied simultaneously with a given large probability. In this paper, we propose to solve the JCCP by a sequence of convex approximations. We show that the solutions of the sequence of approximations converge to a Karush-Kuhn-Tucker (KKT) point of the JCCP under a certain asymptotic regime. Furthermore, we propose to use a gradient-based Monte Carlo method to solve the sequence of convex approximations.

Suggested Citation

  • L. Jeff Hong & Yi Yang & Liwei Zhang, 2011. "Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach," Operations Research, INFORMS, vol. 59(3), pages 617-630, June.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:3:p:617-630
    DOI: 10.1287/opre.1100.0910
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    References listed on IDEAS

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