mlsanityData to 14 Oct 2026

Solving (most) of a set of quadratic equalities: Composite optimization for robust phase retrieval

arXiv 1705.02356 ↗First posted 5 May 2017math.ST cs.IT math.ITcited by 24

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Abstract (arXiv)

We develop procedures, based on minimization of the composition f(x) = h(c(x)) of a convex function h and smooth function c, for solving random collections of quadratic equalities, applying our methodology to phase retrieval problems. We show that the prox-linear algorithm we develop can solve phase retrieval problems---even with adversarially faulty measurements---with high probability as soon as the number of measurements m is a constant factor larger than the dimension n of the signal to be recovered. The algorithm requires essentially no tuning---it consists of solving a sequence of convex problems---and it is implementable without any particular assumptions on the measurements taken. We provide substantial experiments investigating our methods, indicating the practical effectiveness of the procedures and showing that they succeed with high probability as soon as m / n ≥ 2 when the signal is real-valued.

Key facts. Cited by 24 papers in the map (data through 14 Oct 2026). First posted on arXiv 5 May 2017.

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Citing papers per year: 2021: 4; 2022: 3; 2023: 8; 2024: 7; 2025: 0; 2026: 2.

24 papers.

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  1. 2021Rank Overspecified Robust Matrix Recovery: Subgradient Method and Exact Recoverycited by 22
  2. 2021Active manifolds, stratifications, and convergence to local minima in nonsmooth optimizationcited by 11
  3. 2021Minibatch and Momentum Model-based Methods for Stochastic Weakly Convex Optimizationcited by 10
  4. 2021Escaping Saddle Points for Nonsmooth Weakly Convex Functions via Perturbed Proximal Algorithmscited by 4
  5. 2023ReSync: Riemannian Subgradient-based Robust Rotation Synchronizationcited by 3
  6. 2024Stochastic Weakly Convex Optimization Beyond Lipschitz Continuitycited by 3
  7. 2024On the Uniform Convergence of Subdifferentials in Stochastic Optimization and Learningcited by 3
  8. 2023Linearization Algorithms for Fully Composite Optimizationcited by 2
  9. 2023A Unified Analysis on the Subgradient Upper Bounds for the Subgradient Methods Minimizing Composite Nonconvex, Nonsmooth and Non-Lipschitz Functionscited by 2
  10. 2024Robust Gradient Descent for Phase Retrievalcited by 2
  11. 2024Robust Low-rank Tensor Train Recoverycited by 2
  12. 2026Convergence of Spectral Descent for Non-smooth Optimizationcited by 2
12 more
  1. 2022Randomized Coordinate Subgradient Method for Nonsmooth Composite Optimizationcited by 1
  2. 2023A New Inexact Proximal Linear Algorithm with Adaptive Stopping Criteria for Robust Phase Retrievalcited by 1
  3. 2023FedDRO: Federated Compositional Optimization for Distributionally Robust Learningcited by 1
  4. 2023Acceleration and Implicit Regularization in Gaussian Phase Retrievalcited by 1
  5. 2026Tractable Gaussian Phase Retrieval with Heavy Tails and Adversarial Corruption with Near-Linear Sample Complexitycited by 1
  6. 2022Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraintscited by 0
  7. 2022SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimizationcited by 0
  8. 2023An inexact LPA for DC composite optimization and application to matrix completions with outlierscited by 0
  9. 2023Moreau Envelope ADMM for Decentralized Weakly Convex Optimizationcited by 0
  10. 2024Computationally efficient reductions between some statistical modelscited by 0
  11. 2024Smoothed Robust Phase Retrievalcited by 0
  12. 2024ℓ1-norm rank-one symmetric matrix factorization has no spurious second-order stationary pointscited by 0