Adjustable Robust Optimization Models for a Nonlinear Two-Period System |
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Authors: | A Takeda S Taguchi R H Tütüncü |
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Institution: | (1) Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan;(2) Digital Media Network Company, Toshiba Corporation, Tokyo, Japan;(3) Quantitative Investment Strategies, Goldman Sachs Asset Management, New York, NY, USA |
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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 mapping for adjustable variables and present several examples and applications satisfying
these conditions.
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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Keywords: | Robust optimization Two-period nonlinear optimization problem Quasiconvex set valued map |
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