Surrogate duality for robust optimization

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Robust optimization problems, which have uncertain data, are considered. We prove surrogate duality theorems for robust quasiconvex optimization problems and surrogate min-max duality theorems for robust convex opti-mization problems. We give necessary and sufficient constraint qualifications for surrogate duality and surrogate min-max duality, and show some exam-ples at which such duality results are used effectively. Moreover, we obtain a surrogate duality theorem and a surrogate min-max duality theorem for semi-definite optimization problems in the face of data uncertainty.