  Robust optimization methods have shown practical advantages in a wide range
of decision-making applications under uncertainty. Recently, their efficacy has
been extended to multi-period settings. Current approaches model uncertainty
either independent of the past or in an implicit fashion by budgeting the
aggregate uncertainty. In many applications, however, past realizations
directly influence future uncertainties. For this class of problems, we develop
a modeling framework that explicitly incorporates this dependence via connected
uncertainty sets, whose parameters at each period depend on previous
uncertainty realizations. To find optimal here-and-now solutions, we
reformulate robust and distributionally robust constraints for popular set
structures and demonstrate this modeling framework numerically on broadly
applicable knapsack and portfolio-optimization problems.
