We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved are simultaneously diagonizable. This extension of the S-lemma may also be useful for other purposes. We also extend the results to the case of conic quadratic constraints with implementation error. Several applications are discussed, e.g., design centering, robust linear programming with both parameter uncertainty and implementation error, and quadratic decision rules for the adjustable robust optimization problem.
Joint work with A. Ben-Tal
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