A 2-block semi-proximal ADMM for solving the H-weighted nearest correlation matrix problem

作者：Chang, Xiaokai; Liu, Sanyang^*

来源：Optimization, 2017, 66(1): 1-16.

DOI：10.1080/02331934.2016.1246547

• Nearest correlation matrix problem
• alternating direction method of multipliers
• semi-proximal ADMM
• convex quadratic semidefinite programming
• KKT conditions
• convergence analysis

Higham considered two types of nearest correlation matrix (NCM) problems, namely the W-weighted case and the H-weighted case. Since there exists well-defined computable formula for the projection onto the symmetric positive semidefinite cone under the W-weighting, it has been well studied to make several Lagrangian dual-based efficient numerical methods available. But these methods are not applicable for the H-weighted case mainly due to the lack of a computable formula. The H-weighted case remains numerically challenging, especially for the highly ill-conditioned weight matrix H. In this paper, we aim to solve the dual form of the H-weighted NCM problem, which has three separable blocks in the objective function with the second part being linear. Based on the linear part, we reformulate it as a new problem with two separable blocks, and introduce the 2-block semi-proximal alternating direction method of multipliers to deal with it. The efficiency of the proposed algorithms is demonstrated on the random test problems, whose weight matrix H are highly ill-conditioned or rank deficient.

• 出版日期2017
• 单位西安电子科技大学; 兰州理工大学