期刊
IMA JOURNAL OF NUMERICAL ANALYSIS
卷 41, 期 4, 页码 2488-2515出版社
OXFORD UNIV PRESS
DOI: 10.1093/imanum/draa031
关键词
quadratically constrained quadratic programming; semidefinite programming; semidefinite relaxation; penalty function
资金
- Chinese Academy of Sciences
- National Science Foundation [DMR 1534910, CCF1704833]
- National Natural Science Foundation of China [11331012, 11688101]
Quadratically constrained quadratic programming (QCQP) is prevalent in engineering applications, and we have proposed a penalty formulation based on semidefinite relaxation to tackle this NP-hard problem. Our algorithm has been shown to be very effective in finding high-quality solutions through numerical testing on well-studied QCQP problems.
Quadratically constrained quadratic programming (QCQP) appears widely in engineering applications such as wireless communications and networking and multiuser detection with examples like the MAXCUT problem and boolean optimization. A general QCQP problem is NP-hard. We propose a penalty formulation for the QCQP problem based on semidefinite relaxation. Under suitable assumptions we show that the optimal solutions of the penalty problem are the same as those of the original QCQP problem if the penalty parameter is sufficiently large. Then, to solve the penalty problem, we present a proximal point algorithm and an update rule for the penalty parameter. Numerically, we test our algorithm on two well-studied QCQP problems. The results show that our proposed algorithm is very effective in finding high-quality solutions.
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