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论文类型：期刊论文
发表时间：2014-05-04
发表刊物：OPTIMIZATION METHODS & SOFTWARE
收录刊物：EI、SCIE、Scopus
卷号：29
期号：3
页面范围：561-582
ISSN号：1055-6788
关键字：DC programming; correlation matrix; low rank; semi-definite programming; H-weighted; SCA
摘要：Rank-constrained nearest correlation matrix problems, weighted or not, are reformulated into difference of convex (DC) functions constrained optimization problems. A general sequential convex approximation (SCA) approach for a DC-constrained optimization problem is developed. To overcome difficulties encountered in solving the convex approximation subproblems in the SCA approach, an SCA-based nonsmooth equation approach is proposed to solve the specific rank-constrained problem. In this approach, we use a simple iteration scheme for updating the multiplier variable corresponding to the rank constraint, and an inexact smoothing Newton method for calculating the primal variable and the multiplier variable corresponding to the linear constraint. Numerical experiments are reported and they illustrate the efficiency of our approach.