Quadratically adjustable robust linear optimization with inexact data via generalized S-lemma: Exact second-order cone program reformulations

•Studies adjustable robust linear optimization problems with quadratic decision rules.•Incorporates inexactness of the data in the construction of uncertainty sets.•Establishes generalizations of S-Lemma for classes of nonconvex quadratic systems.•Presents exact conic programming reformulations via a generalized S-Lemma.•Illustrates results with numerical experiments on lot-sizing problems with demand uncertainty.