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.
Research Report No. 04-CNA-013, Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA, August 2004