7 citations · 18 across the 17 of their papers we have counts for
19 papers
Globally Convergent Block Coordinate Descent Algorithms for Semi-Nonnegative Independent Component Analysis
Zhenyu Cai, Wentao Ding, Jianze Li +1
We propose a subgradient-based block coordinate descent (BCD-SubG) framework for nonconvex optimization over products of probability simplices and a closed feasible set, motivated…
From Manifold Identification to Newton Acceleration on Intersections: Sparse Stiefel Optimization
Shixiang Chen, Wen Huang
We study a Newton acceleration for sparse composite optimization on the Stiefel manifold. The main difficulty is geometric: the active manifold identified by the nonsmooth regulari…
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…
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…
An increasing rank Riemannian method for generalized Lyapunov equations
Zhenwei Huang, Wen Huang
In this paper, we consider finding a low-rank approximation to the solution of a large-scale generalized Lyapunov matrix equation in the form of , where and…
Riemannian Trust Region Methods for SC Minimization
Chenyu Zhang, Rufeng Xiao, Wen Huang +1
Manifold optimization has recently gained significant attention due to its wide range of applications in various areas. This paper introduces the first Riemannian trust region meth…
A Riemannian Proximal Newton Method
Wutao Si, P. -A. Absil, Wen Huang +2
In recent years, the proximal gradient method and its variants have been generalized to Riemannian manifolds for solving optimization problems with an additively separable structur…
Tensor Completion via Tensor Train Based Low-Rank Quotient Geometry under a Preconditioned Metric
Jian-Feng Cai, Wen Huang, Haifeng Wang +1
This paper investigates the low-rank tensor completion problem, which is about recovering a tensor from partially observed entries. We consider this problem in the tensor train for…
A Riemannian Optimization Approach to Clustering Problems
Wen Huang, Meng Wei, Kyle A. Gallivan +1
This paper considers the optimization problem in the form of where is smooth, $\mathcal{F}_v = \{X \in \mathbb{R}^{n \times q} : X…
Solving Stackelberg Prediction Game with Least Squares Loss via Spherically Constrained Least Squares Reformulation
Jiali Wang, Wen Huang, Rujun Jiang +2
The Stackelberg prediction game (SPG) is popular in characterizing strategic interactions between a learner and an attacker. As an important special case, the SPG with least square…
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…
An Inexact Riemannian Proximal Gradient Method
Wen Huang, Ke Wei
This paper considers the problem of minimizing the summation of a differentiable function and a nonsmooth function on a Riemannian manifold. In recent years, proximal gradient meth…
Recursive Importance Sketching for Rank Constrained Least Squares: Algorithms and High-order Convergence
Yuetian Luo, Wen Huang, Xudong Li +1
In this paper, we propose {\it \underline{R}ecursive} {\it \underline{I}mportance} {\it \underline{S}ketching} algorithm for {\it \underline{R}ank} constrained least squares {\it \…
Riemannian Proximal Gradient Methods (extended version)
Wen Huang, Ke Wei
In the Euclidean setting, the proximal gradient method and its accelerated variants are a class of efficient algorithms for optimization problems with decomposable objective. In th…
An Extension of Fast Iterative Shrinkage-thresholding to Riemannian Optimization for Sparse Principal Component Analysis
Wen Huang, Ke Wei
Sparse principal component analysis (PCA), an important variant of PCA, attempts to find sparse loading vectors when conducting dimension reduction. This paper considers the nonsmo…
Blind Deconvolution by a Steepest Descent Algorithm on a Quotient Manifold
Wen Huang, Paul Hand
In this paper, we propose a Riemannian steepest descent method for solving a blind deconvolution problem. We prove that the proposed algorithm with an appropriate initialization wi…
ManifoldOptim: An R Interface to the ROPTLIB Library for Riemannian Manifold Optimization
Sean Martin, Andrew M. Raim, Wen Huang +1
Manifold optimization appears in a wide variety of computational problems in the applied sciences. In recent statistical methodologies such as sufficient dimension reduction and re…