In recent years, the semidefinite relaxation (SDR) technique has been at the center of some of very exciting developments in the area of signal processing and communications, and it has shown great significance and relevance on a variety of applications. Roughly speaking, SDR is a powerful, computationally efficient approximation technique for a host of very difficult optimization problems. In particular, it can be applied to many nonconvex quadratically constrained quadratic programs (QCQPs) in an almost mechanical fashion, including the following problem:
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This work is supported in part by Hong Kong Research Grants Council (RGC) General Research Funds (GRFs), project numbers CUHK415908, CUHK416908, and CUHK419208; by the Army Research Office, grant number W911NF-09-1-0279; and by the National Science Foundation, grant number CMMI-0726336.