Non-Convex Optimization

Sample-Efficient Geometry Reconstruction from Euclidean Distances using Non-Convex Optimization
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs …
PDF Cite Code arXiv
Linear Convergence of Iteratively Reweighted Least Squares for Nuclear Norm Minimization
Low-rank matrix recovery problems are ubiquitous in many areas of science and engineering. One approach to solve these problems is …
PDF Cite DOI
Learning Transition Operators From Sparse Space-Time Samples
We consider the nonlinear inverse problem of learning a transition operator A from partial observations at T different times, in the …
PDF Cite arXiv
Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares
We propose a new algorithm for the problem of recovering data that adheres to multiple, heterogeneous low-dimensional structures from …
PDF Cite Code Poster Slides Link to Proceedings arXiv OpenReview
On the Convergence of IRLS and Its Variants in Outlier-Robust Estimation
Outlier-robust estimation involves estimating some parameters (e.g., 3D rotations) from data samples in the presence of outliers, and …
PDF Cite Code Poster Slides PDF w/ supplementary material
Global Linear and Local Superlinear Convergence of IRLS for Non-Smooth Robust Regression
We advance both the theory and practice of robust $\ell_p$-quasinorm regression for $p \in (0,1]$ by using novel variants of …
PDF Cite Code Poster arXiv OpenReview
A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samples
We propose an iterative algorithm for low-rank matrix completion that can be interpreted as an iteratively reweighted least squares …
PDF Cite Code Poster Link to Proceedings Slides
Escaping Saddle Points in Ill-Conditioned Matrix Completion with a Scalable Second Order Method
We propose an iterative algorithm for low-rank matrix completion that can be interpreted as both an iteratively reweighted least …
PDF Cite Code
Understanding and Enhancing Data Recovery Algorithms - From Noise-Blind Sparse Recovery to Reweighted Methods for Low-Rank Matrix Optimization
We prove new results about the robustness of noise-blind decoders for the problem of re- constructing a sparse vector from …
PDF Cite mediaTUM
Completion of Structured Low-Rank Matrices via Iteratively Reweighted Least Squares
We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of completing a low-rank matrix that is linearly …
PDF Cite DOI