4 papers · 1 filter
Variational analysis of determinantal varieties
Yan Yang, Bin Gao, Ya-xiang Yuan
Determinantal varieties -- the sets of bounded-rank matrices or tensors -- have attracted growing interest in low-rank optimization. The tangent cone to low-rank sets is widely stu…
Distributed Retraction-Free and Communication-Efficient Optimization on the Stiefel Manifold
Yilong Song, Peijin Li, Bin Gao +1
Optimization problems on the Stiefel manifold, ranging from principal component analysis to enhancing neural network robustness, are ubiquitous in machine learning. The Landing alg…
A space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints
Yan Yang, Bin Gao, Ya-xiang Yuan
Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure a…
Desingularization of bounded-rank tensor sets
Bin Gao, Renfeng Peng, Ya-xiang Yuan
Low-rank tensors appear to be prosperous in many applications. However, the sets of bounded-rank tensors are non-smooth and non-convex algebraic varieties, rendering the low-rank o…