62 citations · 186 across the 19 of their papers we have counts for
19 papers
Optimization over the intersection of manifolds
Yan Yang, Bin Gao, Ya-xiang Yuan
Optimization over the intersection of two manifolds arises in a broad range of applications, but is hindered by the coupled geometry of the feasible region. In this paper, we prove…
Nyström Approximation on Manifolds
Hantao Nie, Bin Gao, Andi Han +3
Computations on a manifold often involve constructing an operator on the tangent space and computing its inverse, which can be time-consuming in many applications. In order to redu…
A second-order method landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
Xinhui Xiong, Bin Gao, P. -A. Absil
Retraction-free approaches offer attractive low-cost alternatives to Riemannian methods on the Stiefel manifold, but they are often first-order, which may limit the efficiency unde…
Optimization on product manifolds under a preconditioned metric
Bin Gao, Renfeng Peng, Ya-xiang Yuan
Since optimization on Riemannian manifolds relies on the chosen metric, it is appealing to know that how the performance of a Riemannian optimization method varies with different m…
Infeasible Deterministic, Stochastic, and Variance-Reduction Algorithms for Optimization under Orthogonality Constraints
Pierre Ablin, Simon Vary, Bin Gao +1
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Rie…
Riemannian preconditioned algorithms for tensor completion via tensor ring decomposition
Bin Gao, Renfeng Peng, Ya-xiang Yuan
We propose Riemannian preconditioned algorithms for the tensor completion problem via tensor ring decomposition. A new Riemannian metric is developed on the product space of the mo…
Optimization on the symplectic Stiefel manifold: SR decomposition-based retraction and applications
Bin Gao, Nguyen Thanh Son, Tatjana Stykel
Numerous problems in optics, quantum physics, stability analysis, and control of dynamical systems can be brought to an optimization problem with matrix variable subjected to the s…
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…
Optimization flows landing on the Stiefel manifold
Bin Gao, Simon Vary, Pierre Ablin +1
We study a continuous-time system that solves optimization problems over the set of orthonormal matrices, which is also known as the Stiefel manifold. The resulting optimization fl…
A Random Active Set Method for Strictly Convex Quadratic Problem with Simple Bounds
Ran Gu, Bing Gao
Active set method aims to find the correct active set of the optimal solution and it is a powerful method for solving strictly convex quadratic problem with bound constraints. To g…
A Riemannian rank-adaptive method for low-rank matrix completion
Bin Gao, P. -A. Absil
The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has…
Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric
Bin Gao, Nguyen Thanh Son, P. -A. Absil +1
The symplectic Stiefel manifold, denoted by , is the set of linear symplectic maps between the standard symplectic spaces and $\mathbb{R}^{2n}…
Symplectic eigenvalue problem via trace minimization and Riemannian optimization
Nguyen Thanh Son, P. -A. Absil, Bin Gao +1
We address the problem of computing the smallest symplectic eigenvalues and the corresponding eigenvectors of symmetric positive-definite matrices in the sense of Williamson's theo…
New Riemannian preconditioned algorithms for tensor completion via polyadic decomposition
Shuyu Dong, Bin Gao, Yu Guan +1
We propose new Riemannian preconditioned algorithms for low-rank tensor completion via the polyadic decomposition of a tensor. These algorithms exploit a non-Euclidean metric on th…
Multipliers Correction Methods for Optimization Problems over the Stiefel Manifold
Lei Wang, Bin Gao, Xin Liu
We propose a class of multipliers correction methods to minimize a differentiable function over the Stiefel manifold. The proposed methods combine a function value reduction step w…
An orthogonalization-free parallelizable framework for all-electron calculations in density functional theory
Bin Gao, Guanghui Hu, Yang Kuang +1
All-electron calculations play an important role in density functional theory, in which improving computational efficiency is one of the most needed and challenging tasks. In the m…
Riemannian Optimization on the Symplectic Stiefel Manifold
Bin Gao, Nguyen Thanh Son, P. -A. Absil +1
The symplectic Stiefel manifold, denoted by , is the set of linear symplectic maps between the standard symplectic spaces and $\mathbb{R}^{2n}…
Parallelizable Algorithms for Optimization Problems with Orthogonality Constraints
Bin Gao, Xin Liu, Ya-xiang Yuan
To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability…
On the Łojasiewicz Exponent of the Quadratic Sphere Constrained Optimization Problem
Bin Gao, Xin Liu, Xiaojun Chen +1
In this paper, we prove that the global version of the ojasiewicz gradient inequality holds for quadratic sphere constrained optimization problem with exponent .…