3 citations · 4 across the 6 of their papers we have counts for
5 papers · 1 filter
Simpler flag optimization
Zehua Lai, Lek-Heng Lim, Ke Ye
We study the geometry of flag manifolds under different embeddings into a product of Grassmannians. We show that differential geometric objects and operations -- tangent vector, me…
When geometry meets optimization theory: partially orthogonal tensors
Ke Ye, Shenglong Hu
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employ…
Simpler Grassmannian optimization
Zehua Lai, Lek-Heng Lim, Ke Ye
There are two widely used models for the Grassmannian , as the set of equivalence classes of orthogonal matrices $\operatorname{O}(n)/(\operatorname{O}(k) \…
Linear Convergence of an Alternating Polar Decomposition Method for Low Rank Orthogonal Tensor Approximations
Shenglong Hu, Ke Ye
Low rank orthogonal tensor approximation (LROTA) is an important problem in tensor computations and their applications. A classical and widely used algorithm is the alternating pol…
Optimization on flag manifolds
Ke Ye, Ken Sze-Wai Wong, Lek-Heng Lim
A flag is a sequence of nested subspaces. Flags are ubiquitous in numerical analysis, arising in finite elements, multigrid, spectral, and pseudospectral methods for numerical PDE;…