Iteratively reweighted algorithms are popular methods for solving nonconvex unconstrained minimization problems. Applications are notably mathematical models in image processing or signal processing. They often have a convex subproblem and do not have closed form solutions in general. In this paper, we propose approximate versions of proximal iteratively reweighted algorithms for nonconvex and nonsmooth unconstrained minimization problems. Specifically, we can achieve an approximate solution for the subproblem by applying a computable inexact stopping rule. The convergence of our method is proved based on an inexact unified framework. Numerical applications for image deblurring or denoising problems validate the effectiveness of the proposed algorithms.

迭代重加权算法是解决非凸无约束最小化问题的流行方法。应用尤其是图像处理或信号处理中的数学模型。它们通常具有凸子问题，并且通常没有封闭形式的解决方案。在本文中，我们提出了针对非凸和非平滑无约束最小化问题的近似迭代加权算法的近似版本。具体来说，我们可以通过应用可计算的不精确停止规则来获得子问题的近似解决方案。基于不精确的统一框架证明了我们方法的收敛性。图像去模糊或去噪问题的数值应用验证了所提出算法的有效性。