The non-convex Burer-Monteiro approach works on smooth semidefinite programs
Authors: Nicolas Boumal, Vlad Voroninski, Afonso Bandeira
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Interestingly, known algorithms for optimization on manifolds converge to second-order critical points,2 regardless of initialization [Boumal et al., 2016]. ... Indeed, the numerical experiments clearly show that high accuracy solutions can be computed fast using optimization on manifolds, at least for certain applications. |
| Researcher Affiliation | Academia | Nicolas Boumal Department of Mathematics Princeton University nboumal@math.princeton.edu Vladislav Voroninski Department of Mathematics Massachusetts Institute of Technology vvlad@math.mit.edu Afonso S. Bandeira Department of Mathematics and Center for Data Science Courant Institute of Mathematical Sciences, New York University bandeira@cims.nyu.edu |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper mentions "Manopt, a Matlab toolbox for optimization on manifolds. Journal of Machine Learning Research, 15:1455 1459, 2014. URL http://www.manopt.org." as a tool, but it does not state that the specific code for the methodology described in *this* paper is released or available. |
| Open Datasets | No | The paper mentions problem types like Max-Cut and community detection, and in Appendix B, a "cycle graph of n=20 nodes" is used for a numerical demonstration. However, it does not provide concrete access information (link, DOI, specific citation with authors/year, or repository) for a public dataset used in experiments. |
| Dataset Splits | No | The paper does not specify dataset splits (e.g., training, validation, test percentages or counts) needed to reproduce data partitioning. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper mentions "Manopt [Boumal et al., 2014]", "CVX: Matlab software for disciplined convex programming", and "SDPT3 a MATLAB software package for semideļ¬nite programming", but does not provide specific version numbers for these software dependencies (e.g., "Manopt vX.Y", "CVX 2.1", "SDPT3 4.0"). |
| Experiment Setup | Yes | We use the Riemannian trust-region method as implemented in Manopt [Boumal et al., 2014], with default parameters for the trust-region subproblem, and stopping criterion gradnorm < 10^-8. |