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Stochastic Programming with Equilibrium Constraints

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  • A. Shapiro

    (Georgia Institute of Technology)

Abstract

In this paper, we discuss here-and-now type stochastic programs with equilibrium constraints. We give a general formulation of such problems and study their basic properties such as measurability and continuity of the corresponding integrand functions. We discuss also the consistency and rate of convergence of sample average approximations of such stochastic problems

Suggested Citation

  • A. Shapiro, 2006. "Stochastic Programming with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 221-243, January.
    • Handle: RePEc:spr:joptap:v:128:y:2006:i:1:d:10.1007_s10957-005-7566-x
    DOI: 10.1007/s10957-005-7566-x
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    Cited by:

    1. Patriksson, Michael, 2008. "On the applicability and solution of bilevel optimization models in transportation science: A study on the existence, stability and computation of optimal solutions to stochastic mathematical programs," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 843-860, December.
    2. C. Cromvik & M. Patriksson, 2010. "On the Robustness of Global Optima and Stationary Solutions to Stochastic Mathematical Programs with Equilibrium Constraints, Part 1: Theory," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 461-478, March.
    3. Akshit Goyal & Yiling Zhang & Chuan He, 2023. "Decision Rule Approaches for Pessimistic Bilevel Linear Programs Under Moment Ambiguity with Facility Location Applications," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1342-1360, November.

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