# Frank-Wolfe Works for Non-Lipschitz Continuous Gradient Objectives: Scalable Poisson Phase Retrieval

arXiv: https://arxiv.org/abs/1602.00724 · HTML: https://mlsanity.com/paper/1602.00724/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2016.

## Built on by (most cited first, 4 of 4)

- [First-Order Methods for Convex Optimization](https://mlsanity.com/paper/2101.00935/) (2021)
- [Low-Rank Extragradient Method for Nonsmooth and Low-Rank Matrix Optimization Problems](https://mlsanity.com/paper/2202.04026/) (2022)
- [Scalable Frank-Wolfe on Generalized Self-concordant Functions via Simple Steps](https://mlsanity.com/paper/2105.13913/) (2021)
- [Low-Rank Mirror-Prox for Nonsmooth and Low-Rank Matrix Optimization Problems](https://mlsanity.com/paper/2206.11523/) (2022)

## Abstract (arXiv)

We study a phase retrieval problem in the Poisson noise model. Motivated by the PhaseLift approach, we approximate the maximum-likelihood estimator by solving a convex program with a nuclear norm constraint. While the Frank-Wolfe algorithm, together with the Lanczos method, can efficiently deal with nuclear norm constraints, our objective function does not have a Lipschitz continuous gradient, and hence existing convergence guarantees for the Frank-Wolfe algorithm do not apply. In this paper, we show that the Frank-Wolfe algorithm works for the Poisson phase retrieval problem, and has a global convergence rate of O(1/t), where t is the iteration counter. We provide rigorous theoretical guarantee and illustrating numerical results.