Alternating direction method for bi-quadratic programming

作者：Hu Sheng Long; Huang Zheng Hai^*

来源：Journal of Global Optimization, 2011, 51(3): 429-446.

DOI：10.1007/s10898-010-9635-4

• Alternating direction method
• Bi-quadratic programming
• Quadratic semidefinite programming

Bi-quadratic programming (Bi-QP for short) was studied systematically in Ling et al. (SIAM J. Optim. 20:1286-1320, 2009) due to its various applications in engineering as well as optimization. Several approximation methods were given in the same paper since it is NP-hard. In this paper, we introduce a quadratic SDP relaxation of Bi-QP and discuss the approximation ratio of the method. In particular, by exploiting the favorite structure of the quadratic SDP relaxation, we propose an alternating direction method for solving such a problem and show that the method is globally convergent without any assumption. Some preliminary numerical results are reported which show the effectiveness of the method proposed in this paper.

• 出版日期2011-11
• 单位天津大学