利用交替方向法求解H权重最近相关系数矩阵问题

ADM for H-weighted nearest correlation matrix problem

由于计算H权重的半正定矩阵锥投影比较困难,目前求解带有H权重的最近相关系数矩阵问题的方法很少且比较复杂.考虑用交替方向法求解该问题,每次迭代只需求解一个有显式解的二次规划问题和一个不带权重的半正定矩阵锥投影,计算简单,易于实现.为提高计算速度,还考虑了改进的交替方向法.此外,通过数值实验对交替方向法与现有方法进行了比较,说明了交替方向法对解决带有H权重的最近相关系数矩阵问题的有效性.

There are few methods for solving H-weighted nearest correlation matrix （HNCM） problem in the literatures.The main reason is that it is difficult to obtain a computable formula for the proj ection of a matrix onto the positive semidefinite matrix cone under the H-weight.The alternating direction method （ADM）is applied for solving HNCM problems.At each iteration,a quadratic program with closed-form solution and a proj ection on positive semidefinite matrix cone without weight are calculated.The method is very simple and easy to be implemented.To speed up the calculation,a modified ADM is also studied.The numerical results show that compared with the existing methods ADM is very efficient for solving HNCM problem.