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On first-order algorithms for $$\ell_{1}/$$nuclear norm minimization. (English) Zbl 1293.65089
This paper reviews recent progress in applications of first-order optimization methods to problems of $$l_1$$/nuclear norm minimization. Two approaches are considered. The first approach presents the constructions of proximal point type algorithms and results related to composite minimization and its application to Lasso problems. The second approach covers the saddle-point first-order algorithms for Dantzig selector problems. The complexity analysis of both approaches are established.

##### MSC:
 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming 65Y20 Complexity and performance of numerical algorithms
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