An Efficient Approach to Solve the Large-Scale Semidefinite Programming Problems

作者：Zheng, Yongbin^*; Yan, Yuzhuang; Liu, Sheng; Huang, Xinsheng; Xu, Wanying

来源：Mathematical Problems in Engineering, 2012, 2012(Pt.1): 764760.

DOI：10.1155/2012/764760

• Brownian motion
• Diffusion processes
• Stochastic control
• Risk sensitivity
• Hitting time
• Stochastic differential equation.

Solving the large-scale problems with semidefinite programming (SDP) constraints is of great importance in modeling and model reduction of complex system, dynamical system, optimal control, computer vision, and machine learning. However, existing SDP solvers are of large complexities and thus unavailable to deal with large-scale problems. In this paper, we solve SDP using matrix generation, which is an extension of the classical column generation. The exponentiated gradient algorithm is also used to solve the special structure subproblem of matrix generation. The numerical experiments show that our approach is efficient and scales very well with the problem dimension. Furthermore, the proposed algorithm is applied for a clustering problem. The experimental results on real datasets imply that the proposed approach outperforms the traditional interior-point SDP solvers in terms of efficiency and scalability.

• 出版日期2012
• 单位中国人民解放军国防科学技术大学; 浙江工业大学