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A Preconditioned Conjugate Gradient Method with Active Set Strategy for $$\ell _1$$ℓ1-Regularized Least Squares

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In the paper, we consider the $$\ell _1$$ℓ1-regularized least square problem which has been intensively involved in the fields of signal processing, compressive sensing, linear inverse problems and statistical inference.… Click to show full abstract

In the paper, we consider the $$\ell _1$$ℓ1-regularized least square problem which has been intensively involved in the fields of signal processing, compressive sensing, linear inverse problems and statistical inference. The considered problem has been proved recently to be equivalent to a nonnegatively constrained quadratic programming (QP). In this paper, we use a recently developed active conjugate gradient method to solve the resulting QP problem. To improve the algorithm’s performance, we design a subspace exact steplength as well as a precondition technique. The performance comparisons illustrate that the proposed algorithm is competitive and even performs little better than several state-of-the-art algorithms.

Keywords: gradient method; ell regularized; conjugate gradient; regularized least

Journal Title: Journal of the Operations Research Society of China
Year Published: 2018

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