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Distributionally Robust Optimization and Its Tractable Approximations

Author

Listed:
  • Joel Goh

    (Stanford Graduate School of Business, and NUS Business School, National University of Singapore, Singapore)

  • Melvyn Sim

    (NUS Business School and NUS Risk Management Institute, National University of Singapore, Singapore)

Abstract

In this paper we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust and more flexible than the standard technique of using linear rules. Our framework begins by first affinely extending the set of primitive uncertainties to generate new linear decision rules of larger dimensions and is therefore more flexible. Next, we develop new piecewise-linear decision rules that allow a more flexible reformulation of the original problem. The reformulated problem will generally contain terms with expectations on the positive parts of the recourse variables. Finally, we convert the uncertain linear program into a deterministic convex program by constructing distributionally robust bounds on these expectations. These bounds are constructed by first using different pieces of information on the distribution of the underlying uncertainties to develop separate bounds and next integrating them into a combined bound that is better than each of the individual bounds.

Suggested Citation

  • Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
  • Handle: RePEc:inm:oropre:v:58:y:2010:i:4-part-1:p:902-917
    DOI: 10.1287/opre.1090.0795
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    References listed on IDEAS

    as
    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Dimitris Bertsimas & Aurélie Thiele, 2006. "A Robust Optimization Approach to Inventory Theory," Operations Research, INFORMS, vol. 54(1), pages 150-168, February.
    3. Karthik Natarajan & Dessislava Pachamanova & Melvyn Sim, 2008. "Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization," Management Science, INFORMS, vol. 54(3), pages 573-585, March.
    4. Xin Chen & Melvyn Sim & Peng Sun, 2007. "A Robust Optimization Perspective on Stochastic Programming," Operations Research, INFORMS, vol. 55(6), pages 1058-1071, December.
    5. Aharon Ben‐Tal & Marc Teboulle, 2007. "An Old‐New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476, July.
    6. 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.
    7. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    8. Aharon Ben-Tal & Marc Teboulle, 1986. "Expected Utility, Penalty Functions, and Duality in Stochastic Nonlinear Programming," Management Science, INFORMS, vol. 32(11), pages 1445-1466, November.
    9. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    10. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    11. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    12. Xin Chen & Yuhan Zhang, 2009. "Uncertain Linear Programs: Extended Affinely Adjustable Robust Counterparts," Operations Research, INFORMS, vol. 57(6), pages 1469-1482, December.
    13. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    14. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    15. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    programming; stochastic;

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