So far, robust optimization have focused on computing solutions resilient to data uncertainty, given an uncertainty set representing the possible realizations of this uncertainty. Here, instead, we are interested in answering the following question: once a solution of a problem is given, which is the largest uncertainty set that this solution can support? We address this question for a popular uncertainty set used in robust optimization, the cardinality constrained one, proving that an answer can be provided in polynomial time.
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