Geometric Certificates for Deterministic Global Linear Convergence of Overparameterized Projected Gradient Descent

Teng Zhang, Xing Fan

We study projected gradient descent (ProjGD) for the rank-constrained problem $\min \{f(X):\mathrm{rank}(X)\le r\}$ when the unconstrained minimizer $X_{\ast }$ has rank $r_{\ast }\le r$…