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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