2010/08/31 by Lu, Zhaosong, Zhang, Yong
#Computational Finance (q-fin.CP) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Statistical Finance (q-fin.ST) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.1008.5373
In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result, we then propose penalty decomposition methods for general rank minimization problems in which each subproblem is solved by a block coordinate descend method. Under some suitable assumptions, we show that any accumulation point of the sequence generated by the penalty decomposition methods satisfies the first-order optimality conditions of a nonlinear reformulation of the problems. Finally, we test the performance of our methods by applying them to the matrix completion and nearest low-rank correlation matrix problems. The computational results demonstrate that our methods are generally comparable or superior to the existing methods in terms of solution quality.