Abstract
While ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -minimization (ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -min) has recently been studied extensively in optimization, the high computational cost associated with the traditional algorithms has largely hindered their application to high-dimensional, large-scale problems. This paper discusses accelerated ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -min techniques using augmented Lagrangian methods and its parallelization leveraging the parallelism available in modern GPU and CPU hardware. The performance of the new algorithms is demonstrated in a robust face recognition application. Through extensive simulation and real-world experiments, we provide useful guidelines about applying fast ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -min on large-scale data for practitioners.
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