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Iterative hard thresholding methods for \(l_0\) regularized convex cone programming. (English) Zbl 1308.65094
The author presents an iterative hard thresholding (IHT) method and its variant for solving a special \(l_0\) regularized box constrained convex programming. The iteration complexity of the IHT method for finding an \(\epsilon\)-local-optimal solution of the problem is obtained. Furthermore, the author develops a method for solving \(l_0\) regularized convex cone programming by applying the IHT method to its quadratic penalty relation and establishes its iteration complexity for finding an \(\epsilon\)-approximate local minimizer of the problem.

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C25 Convex programming
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