9 citations · 16 across the 8 of their papers we have counts for
9 papers
A counterexample to global convergence of classical DFP under the standard strong Wolfe conditions
Benqi Liu, Zichen Wang, Zaiwen Wen +2
A long-standing open question in quasi-Newton optimization asks whether the classical Davidon--Fletcher--Powell (DFP) method converges globally on uniformly convex objectives when…
The Error in Multivariate Linear Extrapolation with Applications to Derivative-Free Optimization
Liyuan Cao, Zaiwen Wen, Ya-xiang Yuan
We study in this paper the function approximation error of multivariate linear extrapolation. The sharp error bound of linear interpolation already exists in the literature. Howeve…
Some Sharp Error Bounds for Multivariate Linear Interpolation and Extrapolation
Liyuan Cao, Zaiwen Wen, Ya-xiang Yuan
We study in this paper the function approximation error of linear interpolation and extrapolation. Several upper bounds are presented along with the conditions under which they are…
A Brief Introduction to Manifold Optimization
Jiang Hu, Xin Liu, Zaiwen Wen +1
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usua…
Low-rank Matrix Optimization Using Polynomial-filtered Subspace Extraction
Yongfeng Li, Haoyang Liu, Zaiwen Wen +1
In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional firs…
Adaptive Low-Nonnegative-Rank Approximation for State Aggregation of Markov Chains
Yaqi Duan, Mengdi Wang, Zaiwen Wen +1
This paper develops a low-nonnegative-rank approximation method to identify the state aggregation structure of a finite-state Markov chain under an assumption that the state space…
Structured Quasi-Newton Methods for Optimization with Orthogonality Constraints
Jiang Hu, Bo Jiang, Lin Lin +2
In this paper, we study structured quasi-Newton methods for optimization problems with orthogonality constraints. Note that the Riemannian Hessian of the objective function require…
A Semi-smooth Newton Method for Solving Semidefinite Programs in Electronic Structure Calculations
Yongfeng Li, Zaiwen Wen, Chao Yang +1
The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-bo…
Adaptive Regularized Newton Method for Riemannian Optimization
Jiang Hu, Andre Milzarek, Zaiwen Wen +1
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration…