In this paper, we investigate the active set identification technique of ISTA and provide some good properties. An active set Newton-CG method is then proposed for ${\ell }_1$ optimization. Under appropriate conditions, we show that the proposed method is globally convergent with some nonmonotone line search. The numerical comparisons with several state-of-art methods demonstrate the efficiency of the proposed method.

中文翻译：

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活跃集牛顿-CG方法ℓ ₁优化

在本文中，我们研究了ISTA的活动集识别技术，并提供了一些良好的性能。然后提出了一种主动集牛顿-CG方法${\ell }_{\mathrm{1个}}$优化。在适当的条件下，我们证明了该方法与某些非单调线搜索是全局收敛的。与几种最新方法的数值比较证明了该方法的有效性。