Robust Solutions of Uncertain Complex-valued Quadratically Constrained Programs  

作　　者：Da Chuan XU Zheng Hai HUANG 

机构地区：[1]Department of Applied Mathematics, College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100022, P. R. China [2]Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第8期1279-1290,共12页数学学报（英文版）

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)

摘　　要：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.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.

关 键 词：robust optimization quadratically constrained program complex semidefinite program S-Lemma 

分 类 号：O224[理学—运筹学与控制论] TP301[理学—数学]