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Center for Nonlinear Studies |
We consider a two-stage adaptive robust optimization problem with linear constraints and uncertain right hand side. This problem arises in many applications including unit-commitment in day-ahead electricity markets, facility location and capacity planning. However, computing an optimal adaptive solution is intractable in general. In fact, the problem is hard to approximate with a factor $\Omega(\log n)$ even for budget of uncertainty sets (an important class of sets to model uncertainty). Affine policies, where recourse decisions are constrained to be affine functions of the uncertain parameters, have been widely studied as an approximation approach and have a good empirical performance. This work aims to provide a tight theoretical characterization of the power and limitations of affine policies. In particular, we show that surprisingly affine policies provide the best possible approximation for budget of uncertainty sets that nearly matches the hardness lower bound. We also discuss generalizations to the case when the uncertainty set is given by multiple knapsack constraints. This is based on joint work with Omar El Housni.
Host: Michael Chertkov