Some first order algorithms for `1/nuclear norm minimization

In the last decade, the problems related to l1/nuclear norm minimization attract a lot of attention in Signal Processing, Machine Learning and Optimization communities. In this paper, devoted to `1/nuclear norm minimization as “optimization beasts,” we give a detailed description of two attractive First Order optimization techniques for solving the problems of this type. The first one, aimed primarily at Lasso type problems, is the Fast Gradient Methods as applied to Composite Minimization formulations. The second approach, aimed at Dantzig Selector type problems, utilizes saddle point First Order algorithms and reformulation of the problem of interest as generalized bilinear saddle point problem. For both approaches, we give complete and detailed complexity analysis and discuss the application domains.