This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions are two adaptive stopping criteria for the subproblem. The convergence behavior of the proposed methods is analyzed. Through experiments on both synthetic and real datasets, we demonstrate that our methods are much more efficient than existing methods, such as the original proximal linear algorithm and the subgradient method.

翻译：本文考虑鲁棒相位恢复问题，该问题可建模为非光滑非凸优化问题。我们提出一种新型非精确近端线性算法，其子问题采用非精确求解方式。本文的贡献在于为子问题设计了两种自适应停止准则，并分析了所提出方法的收敛特性。通过在合成数据集与真实数据集上的实验，我们证明该方法比现有方法（如原始近端线性算法与次梯度方法）具有更高的计算效率。