# A New Inexact Proximal Linear Algorithm with Adaptive Stopping Criteria for Robust Phase Retrieval

arXiv: https://arxiv.org/abs/2304.12522 · HTML: https://mlsanity.com/paper/2304.12522/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 25 Apr 2023.

## Builds on (most cited first, 15 of 15)

- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [Efficiency of minimizing compositions of convex functions and smooth maps](https://mlsanity.com/paper/1605.00125/) (2016)
- [Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems](https://mlsanity.com/paper/1505.05114/) (2015)
- [Stochastic Methods for Composite and Weakly Convex Optimization Problems](https://mlsanity.com/paper/1703.08570/) (2017)
- [Subgradient methods for sharp weakly convex functions](https://mlsanity.com/paper/1803.02461/) (2018)
- [Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence](https://mlsanity.com/paper/1904.10020/) (2019)
- [Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow](https://mlsanity.com/paper/1605.08285/) (2016)
- [Solving (most) of a set of quadratic equalities: Composite optimization for robust phase retrieval](https://mlsanity.com/paper/1705.02356/) (2017)
- [Optimal Convergence Rates for the Proximal Bundle Method](https://mlsanity.com/paper/2105.07874/) (2021)
- [A Manifold Proximal Linear Method for Sparse Spectral Clustering with Application to Single-Cell RNA Sequencing Data Analysis](https://mlsanity.com/paper/2007.09524/) (2020)
- [Inexact Successive Quadratic Approximation for Regularized Optimization](https://mlsanity.com/paper/1803.01298/) (2018)
- [Primal-Dual Rates and Certificates](https://mlsanity.com/paper/1602.05205/) (2016)
- [Composite optimization for robust blind deconvolution](https://mlsanity.com/paper/1901.01624/) (2019)
- [Variable metric inexact line-search based methods for nonsmooth optimization](https://mlsanity.com/paper/1506.00385/) (2015)
- [Inexact Variable Metric Stochastic Block-Coordinate Descent for Regularized Optimization](https://mlsanity.com/paper/1807.09146/) (2018)

## Built on by (most cited first, 1 of 1)

- [Smoothed Robust Phase Retrieval](https://mlsanity.com/paper/2409.01570/) (2024)

## Abstract (arXiv)

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.