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 ell...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.展开更多
基金NsF of China (Grant No.60773185,10401038)Program for Beijing Excellent Talents and NSF of China (Grant No.10571134)the Natural Science Foundation of Tianjin (Grant No.07JCYBJC05200)
文摘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.
