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：本文考虑稳健相位恢复问题，该问题可表述为一个非光滑、非凸优化问题。我们提出了一种新的非精确近端线性算法，其中子问题被非精确求解。本文的贡献在于为子问题设计了两种自适应停止准则。所提方法的收敛行为得到了分析。通过在合成数据集和真实数据集上的实验，我们证明了所提方法比现有方法（如原始近端线性算法和次梯度方法）效率更高。