Rank Overparameterization in the Nonconvex Low-Rank Factorization: Global Optimality and Large-Scale Algorithms
Abstract
Rank Overparameterization in the Nonconvex Low-Rank Factorization: Global Optimality and Large-Scale Algorithms Richard Y. Zhang (ryz@illinois.edu)The nonconvex low-rank factorization of Burer and Monteiro promises to reliably and accurately solve large-scale convex semidefinite optimization problems, with broad impact across numerous domains of Navy interest. However, our current theoreticalunderstanding remains limited to highly idealized scenarios, and a heuristic application of the approach in practice often proves ineffective and/or uncompetitive on real-world datasets. This proposal outlines a three-year program to address these existing gaps and deficiencies, motivated by the PI s recent theoretical and algorithmic advances on rank overparameterization, which in the easiercase of unconstrained optimization, have already resulted in significant progress. We believe that rank overparameterization will be the key idea that addresses existing gaps and deficiencies in the much harder#but also much more impactful#case of constrained optimization.Approved for Public Release
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Nov 09, 2024
- Source ID
- N000142412671
Entities
People
- Richard Zhang
Organizations
- Office of Naval Research
- United States Navy
- University of Illinois Urbana–Champaign