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Adjustable Robust Optimization Models for a Nonlinear Two-Period System

Author

Listed:
  • A. Takeda

    (Tokyo Institute of Technology)

  • S. Taguchi

    (Toshiba Corporation)

  • R. H. Tütüncü

    (Goldman Sachs Asset Management)

Abstract

We study two-period nonlinear optimization problems whose parameters are uncertain. We assume that uncertain parameters are revealed in stages and model them using the adjustable robust optimization approach. For problems with polytopic uncertainty, we show that quasiconvexity of the optimal value function of certain subproblems is sufficient for the reducibility of the resulting robust optimization problem to a single-level deterministic problem. We relate this sufficient condition to the cone-quasiconvexity of the feasible set mapping for adjustable variables and present several examples and applications satisfying these conditions.

Suggested Citation

  • A. Takeda & S. Taguchi & R. H. Tütüncü, 2008. "Adjustable Robust Optimization Models for a Nonlinear Two-Period System," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 275-295, February.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:2:d:10.1007_s10957-007-9288-8
    DOI: 10.1007/s10957-007-9288-8
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    References listed on IDEAS

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    3. Joël Benoist & Nicolae Popovici, 2003. "Characterizations of convex and quasiconvex set-valued maps," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 427-435, August.
    4. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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    Cited by:

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    3. Marandi, Ahmadreza & den Hertog, Dick, 2015. "When are Static and Adjustable Robust Optimization with Constraint-Wise Uncertainty Equivalent?," Discussion Paper 2015-045, Tilburg University, Center for Economic Research.
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    6. Dajun Yue & Jiyao Gao & Bo Zeng & Fengqi You, 2019. "A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs," Journal of Global Optimization, Springer, vol. 73(1), pages 27-57, January.
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    8. Yanıkoğlu, İhsan & Gorissen, Bram L. & den Hertog, Dick, 2019. "A survey of adjustable robust optimization," European Journal of Operational Research, Elsevier, vol. 277(3), pages 799-813.

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