Global Landscape of Non-Convex Matrix Sensing
§ Problem Statement
Setup
Unsolved Problem
§ Discussion
§ Significance & Implications
§ Known Partial Results
§ References
Global optimality of local search for low rank matrix recovery
Srinadh Bhojanapalli, Behnam Neyshabur, Nathan Srebro (2016)
NeurIPS
📍 Section 1 (Introduction), paragraph stating prior work “do[es] not tackle the question of the existence of spurious local minima” and random-initialization gap, p. 2 (resolved formally in Section 3, Theorem 3.1, p. 3).
A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
Samuel Burer, Renato D. C. Monteiro (2003)
Mathematical Programming
📍 Section 1 (Introduction), formulation of the low-rank factorization XXᵀ approach to SDP relaxations, pp. 329–331.
Deterministic guarantees for Burer–Monteiro factorizations of smooth semidefinite programs
Nicolas Boumal, Vlad Voroninski, Afonso S. Bandeira (2020)
Communications on Pure and Applied Mathematics
📍 Section 1 (Introduction), Theorem 1.3 (no spurious second-order critical points when factorization rank exceeds √(2m)), p. 316.