期刊
IEEE SIGNAL PROCESSING LETTERS
卷 22, 期 7, 页码 804-808出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LSP.2014.2370033
关键词
Feasible point pursuit; linearization; multicast beamforming; non-convex QCQP; semi-definite relaxation; successive convex approximation
资金
- National Science Foundation [ECCS-1231504, AST-1247885, IIS-1247632]
- Division Of Astronomical Sciences
- Direct For Mathematical & Physical Scien [1247885] Funding Source: National Science Foundation
- Div Of Electrical, Commun & Cyber Sys
- Directorate For Engineering [1231504] Funding Source: National Science Foundation
- Div Of Information & Intelligent Systems
- Direct For Computer & Info Scie & Enginr [1247632] Funding Source: National Science Foundation
Quadratically constrained quadratic programs QCQPs) have a wide range of applications in signal processing and wireless communications. Non-convex QCQPs are NP-hard in general. Existing approaches relax the non-convexity using semi-definite relaxation SDR) or linearize the non-convex part and solve the resulting convex problem. However, these techniques are seldom successful in even obtaining a feasible solution when the QCQP matrices are indefinite. In this letter, a new feasible point pursuit successive convex approximation FPP-SCA) algorithm is proposed for non-convex QCQPs. FPP-SCA linearizes the non-convex parts of the problem as conventional SCA does, but adds slack variables to sustain feasibility, and a penalty to ensure slacks are sparingly used. When FPP-SCA is successful in identifying a feasible point of the non-convex QCQP, convergence to a Karush-Kuhn-Tucker KKT) point is thereafter ensured. Simulations show the effectiveness of our proposed algorithm in obtaining feasible and near-optimal solutions, significantly outperforming existing approaches.
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