  In this work, we design primal and dual bounding methods for multistage
adjustable robust optimization (MSARO) problems by adapting two decision rules
rooted in the stochastic programming literature. This approach approximates the
primal and dual formulations of an MSARO problem with two-stage models. From
the primal perspective, this is achieved by applying two-stage decision rules
that restrict the functional forms of a certain subset of decision variables.
We present sufficient conditions under which the well-known
constraint-and-column generation algorithm can be used to solve the primal
approximation with finite convergence guarantees. From the dual side, we
introduce a distributionally robust dual problem for MSARO models using their
nonanticipative Lagrangian dual and then apply linear decision rules on the
Lagrangian multipliers. For this dual approximation, we present a monolithic
bilinear program valid for continuous recourse problems, and a cutting-plane
method for mixed-integer recourse problems. Our framework is general-purpose
and does not require strong assumptions such as a stage-wise independent
uncertainty set, and can consider integer recourse variables. Computational
experiments on newsvendor, location-transportation, and capital budgeting
problems show that our bounds yield considerably smaller optimality gaps
compared to the existing methods.
