Consider an uncertain constraint aTx b, where aao+u, ||u|| 1. In other words, we have a linear

Consider an uncertain constraint aTx

b, where

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aao+u, ||u|| 1. In other words, we have a linear inequality where the data vector a is uncertain, but rather than giving a stochastic characterization, we assume that it lies within an uncertainty set. The nominal value is ao, and the uncertainty set is a simple box around the nominal value. The feasible set is the collection of points x, such that the inequality is satisfied for every a in the uncertainty set. This kind of constraint, as we shall see later, is common in robust optimization, and it can be generalized to data matrices; see Section 14.4.1 for its relationship with regularized regression.