5 papers
On computing Goldstein approximate second-order stationary points of structured nonsmooth nonconvex programs
Jiewen Guan, Anthony Man-Cho So
In this paper, we exhibit a randomized first-order algorithm to compute Goldstein approximate second-order stationary points of -smooth functions, using tools from randomized sm…
On the hardness of deterministic second-order optimization of functions with Lipschitz gradients
Jiewen Guan, Anthony Man-Cho So
We show that no deterministic zero-respecting algorithm (resp., (general) deterministic algorithm) can compute Goldstein approximate second-order stationary points of functions wit…
On decomposability and subdifferential of the tensor nuclear norm
Jiewen Guan, Bo Jiang, Zhening Li
We study the decomposability and the subdifferential of the tensor nuclear norm. Both concepts are well understood and widely applied in matrices but remain unclear for higher-orde…
-norm rank-one symmetric matrix factorization has no spurious second-order stationary points
Jiewen Guan, Anthony Man-Cho So
This paper studies the nonsmooth optimization landscape of the -norm rank-one symmetric matrix factorization problem using tools from second-order variational analysis. Spe…
On subdifferential chain rule of matrix factorization and beyond
Jiewen Guan, Anthony Man-Cho So
In this paper, we study equality-type Clarke subdifferential chain rules of matrix factorization and factorization machine. Specifically, we show for these problems that provided t…