  This paper presents a novel transformation-proximal bundle algorithm for
multistage adaptive robust optimization problems. By partitioning recourse
decisions into state and control decisions, the proposed algorithm applies
affine control policy only to state decisions and allows control decisions to
be fully adaptive, thus transforming the original problem into an equivalent
two-stage Adaptive Robust Optimization (ARO) problem. Importantly, this
multi-to-two transformation is general enough to be employed with any two-stage
ARO solution algorithms, thus opening a new avenue for a variety of multistage
ARO algorithms. The proximal bundle method is developed for the resulting
two-stage problem along with convergence analysis. In an inventory control
application, the affine disturbance-feedback control policy suffers from a
severe suboptimality with an average gap of 34.88%, while the proposed
algorithm generates an average gap of merely 1.68%.
