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Adjustable Robust Optimization Models for a Nonlinear Two-Period System

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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 map** for adjustable variables and present several examples and applications satisfying these conditions.

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Authors and Affiliations

  1. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan

    A. Takeda

  2. Digital Media Network Company, Toshiba Corporation, Tokyo, Japan

    S. Taguchi

  3. Quantitative Investment Strategies, Goldman Sachs Asset Management, New York, NY, USA

    R. H. Tütüncü

Authors
  1. A. Takeda
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  2. S. Taguchi
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  3. R. H. Tütüncü
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Corresponding author

Correspondence to A. Takeda.

Additional information

Communicated by F.A. Potra.

This work was partially supported by the National Science Foundation, Grants CCR-9875559 and DMS-0139911, and by Grant-in-Aid for Scientific Research from the Ministry of Education, Sports, Science and Culture of Japan, Grant 16710110.

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Takeda, A., Taguchi, S. & Tütüncü, R.H. Adjustable Robust Optimization Models for a Nonlinear Two-Period System. J Optim Theory Appl 136, 275–295 (2008). https://doi.org/10.1007/s10957-007-9288-8

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  • DOI: https://doi.org/10.1007/s10957-007-9288-8

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