Adjustable robust optimization allows for some variables to depend upon the uncertain data
after its realization. However, the uncertainty is often not revealed exactly. Incorporating
inexactness of the revealed data in the construction of ellipsoidal uncertainty sets, we
present an exact second-order cone program reformulation for robust linear optimization
problems with inexact data and quadratically adjustable variables. This is achieved by
establishing a generalization of the celebrated S-lemma for a separable quadratic inequality …