From the 1 of 5 linked papers with an AI index.
7 papers
A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds
Chunming Tang, Hao He, Wen Huang +2
The quadratic optimization-free (QO-free) method is a class of powerful and effective algorithms for solving nonlinearly constrained optimization problems in Euclidean spaces. The…
From Manifold Identification to Newton Acceleration on Intersections: Sparse Stiefel Optimization
Shixiang Chen, Wen Huang
The paper develops a Newton‑accelerated algorithm (MIX) for sparse composite optimization on the Stiefel manifold, handling both transverse and non‑transverse intersections by iden…
Diffeomorphic Logarithm of Special Orthogonal Matrices
Zhifeng Deng, P. -A. Absil, Kyle A. Gallivan +1
The special orthogonal group is a Lie group whose geometry and local structure are encoded by the exponential map in its Lie algebra , the set of s…
Retractions by Alternating Projections
Shixiang Chen, Yixiao He, Wen Huang
Alternating projections and their variants are classical tools for computing points in intersections of sets. Existing analyses for smooth manifolds mainly focus on local convergen…
Riemannian optimization using three different metrics for Hermitian PSD fixed-rank constraints: an extended version
Shixin Zheng, Wen Huang, Bart Vandereycken +1
For smooth optimization problems with a Hermitian positive semi-definite fixed-rank constraint, we consider three existing approaches including the simple Burer--Monteiro method, a…
On the analysis of optimization with fixed-rank matrices: a quotient geometric view
Shuyu Dong, Bin Gao, Wen Huang +1
We study a type of Riemannian gradient descent (RGD) algorithm, designed through Riemannian preconditioning, for optimization on -- the set of $m\times…