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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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    1. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
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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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    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2018. "Minimizing Piecewise-Concave Functions Over Polyhedra," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 580-597, May.
    3. Zhongshun Shi & Siyang Gao & Hui Xiao & Weiwei Chen, 2019. "A worst‐case formulation for constrained ranking and selection with input uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 648-662, December.
    4. 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.
    5. Takano, Yuichi & Gotoh, Jun-ya, 2023. "Dynamic portfolio selection with linear control policies for coherent risk minimization," Operations Research Perspectives, Elsevier, vol. 10(C).
    6. Fanzeres, Bruno & Ahmed, Shabbir & Street, Alexandre, 2019. "Robust strategic bidding in auction-based markets," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1158-1172.
    7. Abbas Khademi & Ahmadreza Marandi & Majid Soleimani-damaneh, 2024. "A new dual-based cutting plane algorithm for nonlinear adjustable robust optimization," Journal of Global Optimization, Springer, vol. 89(3), pages 559-595, July.
    8. Nicolas Kämmerling & Jannis Kurtz, 2020. "Oracle-based algorithms for binary two-stage robust optimization," Computational Optimization and Applications, Springer, vol. 77(2), pages 539-569, November.
    9. 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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