General nonconvex optimization is undoubtedly hard — in sharp contrast to convex optimization, of which there is good separation of problem structure, input data, and optimization algorithms. But many nonconvex problems of interest become amenable to simple and practical algorithms and rigorous analyses once the artificial separation is removed. This page collects recent research effort in this line. (Update: Dec 11 2021)

[S] indicates my contribution.

[New] A BibTex file for papers listed on the page can be downloaded HERE!


Review Articles


Problems with Hidden Convexity or Analytic Solutions

Blind Deconvolution

Separable Nonnegative Matrix Factorization (NMF)

Problems with Provable Global Results

Matrix Completion/Sensing

(See also low-rank matrix/tensor recovery )

Tensor Recovery/Decomposition & Hidden Variable Models

Phase Retrieval

Dictionary Learning

(See also Theory part in Dictionary/Deep Learning)

Deep Learning

Sparse Vectors in Linear Subspaces

(See Structured Element Pursuit )

Nonnegative/Sparse Principal Component Analysis

Mixed Linear Regression

Blind Deconvolution/Calibration

Super Resolution

Synchronization Problems/Community Detection

Joint Alignment

Numerical Linear Algebra

Bayesian Inference

Empirical Risk Minimization & Shallow Networks

System Identification

Burer-Monteiro Style Decomposition Algorithms

Generic Structured Problems

Nonconvex Feasibility Problems

Of Statistical Nature …

Relevant Optimization Methods, Theory, Miscs

Disclaimer - This page is meant to serve a hub for references on this problem, and does not represent in any way personal endorsement of papers listed here. So I do not hold any responsibility for quality and technical correctness of each paper listed here. The reader is advised to use this resource with discretion.

If you’d like your paper to be listed here - Just drop me a few lines via email (which can be found on “Welcome” page). If you don’t bother to spend a word, just deposit your paper on arXiv. I get email alert about new animals there every morning,  and will be happy to hunt one for this zoo if it seems fit.

Special thanks to: Damek Davis, Wotao Yin, Vladislav Voroninski, David Martinez