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A Polynomial-Time Solution Scheme for Quadratic Stochastic Programs

Author

Listed:
  • Paula Rocha

    (Imperial College London)

  • Daniel Kuhn

    (Imperial College London)

Abstract

We consider quadratic stochastic programs with random recourse—a class of problems which is perceived to be computationally demanding. Instead of using mainstream scenario tree-based techniques, we reduce computational complexity by restricting the space of recourse decisions to those linear and quadratic in the observations, thereby obtaining an upper bound on the original problem. To estimate the loss of accuracy of this approach, we further derive a lower bound by dualizing the original problem and solving it in linear and quadratic recourse decisions. By employing robust optimization techniques, we show that both bounding problems may be approximated by tractable conic programs.

Suggested Citation

  • Paula Rocha & Daniel Kuhn, 2013. "A Polynomial-Time Solution Scheme for Quadratic Stochastic Programs," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 576-589, August.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:2:d:10.1007_s10957-012-0264-6
    DOI: 10.1007/s10957-012-0264-6
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    References listed on IDEAS

    as
    1. Angelos Georghiou & Wolfram Wiesemann & Daniel Kuhn, 2010. "Generalized Decision Rule Approximations for Stochastic Programming via Liftings," Working Papers 043, COMISEF.
    2. S. E. Wright, 1994. "Primal-Dual Aggregation and Disaggregation for Stochastic Linear Programs," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 893-908, November.
    3. Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
    4. Xin Chen & Melvyn Sim & Peng Sun & Jiawei Zhang, 2008. "A Linear Decision-Based Approximation Approach to Stochastic Programming," Operations Research, INFORMS, vol. 56(2), pages 344-357, April.
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