In this paper, we develop a simple yet effective screening rule strategy to improve the computational efficiency in solving structured optimization involving nonconvex $\ell_{q,p}$ regularization. Based on an iteratively reweighted $\ell_1$ (IRL1) framework, the proposed screening rule works like a preprocessing module that potentially removes the inactive groups before starting the subproblem solver, thereby reducing the computational time in total. This is mainly achieved by heuristically exploiting the dual subproblem information during each iteration.Moreover, we prove that our screening rule can remove all inactive variables in a finite number of iterations of the IRL1 method. Numerical experiments illustrate the efficiency of our screening rule strategy compared with several state-of-the-art algorithms.

中文翻译：

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一种涉及非凸$\ell_{q,p}$正则化的结构化优化筛选策略

在本文中，我们开发了一种简单而有效的筛选规则策略，以提高解决涉及非凸 $\ell_{q,p}$ 正则化的结构化优化的计算效率。基于迭代重新加权的 $\ell_1$ (IRL1) 框架，所提出的筛选规则就像一个预处理模块，在启动子问题求解器之前可能会移除非活动组，从而减少总计算时间。这主要是通过在每次迭代期间启发式地利用对偶子问题信息来实现的。此外，我们证明了我们的筛选规则可以在IRL1方法的有限次迭代中去除所有不活跃的变量。与几种最先进的算法相比，数值实验说明了我们的筛选规则策略的效率。