Robust solutions of uncertain complex-valued quadratically constrained programs

In this paper, we discuss complex convex quadratically constrained optimization with uncertain data. Using S-Lemma, we show that the robust counterpart of complex convex quadratically constrained optimization with ellipsoidal or intersection-of-two-ellipsoids uncertainty set leads to a complex semidefinite program. By exploring the approximate S-Lemma, we give a complex semidefinite program which approximates the NP-hard robust counterpart of complex convex quadratic optimization with intersection-of-ellipsoids uncertainty set. Research supported by NSF of China (Grant No. 60773185, 10401038) and Program for Beijing Excellent Talents and NSF of China (Grant No. 10571134) and the Natural Science Foundation of Tianjin (Grant No. 07JCYBJC05200)