Inexact Accelerated Proximal Gradient Algorithms For Matrix l_{2,1}-Norm Minimization Problem in Multi-Task Feature Learning

Yaping Hu, Zengxin Wei, Gonglin Yuan
2014 Statistics, Optimization and Information Computing  
In this paper, we extend the implementable APG method to solve the matrix l 2,1 -norm minimization problem arising in multi-task feature learning. We investigate that the resulting inner subproblem has closed-form solution which can be easily determined by taking the problem's favorable structures. Under suitable conditions, we can establish a comprehensive convergence result for the proposed method. Furthermore, we present three different inexact APG algorithms by using the Lipschitz constant,
more » ... the eigenvalue of Hessian matrix and the Barzilai and Borwein parameter in the inexact model, respectively. Numerical experiments on simulated data and real data set are reported to show the efficiency of proposed method.
doi:10.19139/106 fatcat:ubpp2fgznvd47cseux3syl3lfi