Quartic First-Order Methods for Low-Rank Minimization

We study a general nonconvex formulation for low-rank minimization problems. use recent results on non-Euclidean first-order methods to provide efficient and scalable algorithms. Our approach uses the geometry induced by Bregman divergence of well-chosen kernel functions; unconstrained problems, we introduce novel family Gram quartic kernels that improve numerical performance. Numerical experiments Euclidean distance matrix completion symmetric nonnegative factorization show our algorithms scale well reach state-of-the-art performance when compared specialized methods.