The penalty decomposition method is an effective and versatile method for sparse optimization and has been successfully applied to solve compressed sensing, sparse logistic regression, sparse inverse covariance selection, low rank minimization, image restoration, and so on. With increase in the penalty parameters, a sequence of penalty subproblems required being solved by the penalty decomposition method may be time consuming. In this paper, an acceleration of the penalty decomposition method is proposed for the sparse optimization problem. For each penalty parameter, this method just finds some inexact solutions to those subproblems. Computational experiments on a number of test instances demonstrate the effectiveness and efficiency of the proposed method in accurately generating sparse and redundant representations of one-dimensional random signals.

中文翻译：

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一种稀疏优化的不精确惩罚分解方法

惩罚分解方法是一种有效且通用的稀疏优化方法，已成功应用于解决压缩感知、稀疏逻辑回归、稀疏逆协方差选择、低秩最小化、图像恢复等问题。随着惩罚参数的增加，需要通过惩罚分解方法解决的一系列惩罚子问题可能很耗时。本文针对稀疏优化问题提出了一种加速惩罚分解方法。对于每个惩罚参数，该方法只是为这些子问题找到一些不精确的解决方案。