Adjustable Robust Optimization Models for Nonlinear Multi-Period Optimization



Akiko Takeda
Dept. of Mathematical \& Computing Sciences
Tokyo Institute of Technology Tokyo, Japan
takeda@is.titech.ac.jp


Shunsuke Taguchi
Dept. of Mathematical \& Computing Sciences
Tokyo Institute of Technology Tokyo, Japan
taguchi0@is.titech.ac.jp

and



Reha H. Tütüncü
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
reha@cmu.edu



We study multi-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 quasi-convexity 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 quasi cone-convexity of the feasible set mapping for adjustable variables and provide several examples satisfying these conditions.

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