62 citations · 151 across the 21 of their papers we have counts for
22 papers
The Sharp Worst-Case Asymptotic Rate of the Barzilai--Borwein Method in and Hilbert Spaces
Shutai Yang, Ya-Xiang Yuan
We establish sharp asymptotic rates for the two Barzilai--Borwein (BB) rules on uniformly positive quadratics and local nonlinear problems. In finite dimensions, for either fixed r…
A New Two-dimensional Model-based Subspace Method for Large-scale Unconstrained Derivative-free Optimization: 2D-MoSub
Pengcheng Xie, Ya-xiang Yuan
This paper proposes the method 2D-MoSub (2-dimensional model-based subspace method), which is a novel derivative-free optimization (DFO) method based on the subspace method for gen…
Analysis Accelerated Mirror Descent via High-resolution ODEs
Ya-xiang Yuan, Yi Zhang
Mirror descent plays a crucial role in constrained optimization and acceleration schemes, along with its corresponding low-resolution ordinary differential equations (ODEs) framewo…
Symplectic Discretization Approach for Developing New Proximal Point Algorithm
Ya-xiang Yuan, Yi Zhang
The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the…
Linear convergence of forward-backward accelerated algorithms without knowledge of the modulus of strong convexity
Bowen Li, Bin Shi, Ya-xiang Yuan
A significant milestone in modern gradient-based optimization was achieved with the development of Nesterov's accelerated gradient descent (NAG) method. This forward-backward techn…
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…
On Underdamped Nesterov's Acceleration
Shuo Chen, Bin Shi, Ya-xiang Yuan
The high-resolution differential equation framework has been proven to be tailor-made for Nesterov's accelerated gradient descent method~(\texttt{NAG}) and its proximal corresponde…
Least Norm Updating Quadratic Interpolation Model Function for Derivative-free Trust-region Algorithms
Pengcheng Xie, Ya-xiang Yuan
Derivative-free optimization methods are numerical methods for optimization problems in which no derivative information is used. Such optimization problems are widely seen in many…
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…
Derivative-Free Optimization with Transformed Objective Functions (DFOTO) and the Algorithm Based on the Least Frobenius Norm Updating Quadratic Model
Pengcheng Xie, Ya-xiang Yuan
Derivative-free optimization problems are optimization problems where derivative information is unavailable. The least Frobenius norm updating quadratic interpolation model functio…
Linear Convergence of ISTA and FISTA
Bowen Li, Bin Shi, Ya-xiang Yuan
In this paper, we revisit the class of iterative shrinkage-thresholding algorithms (ISTA) for solving the linear inverse problem with sparse representation, which arises in signal…
Revisiting the acceleration phenomenon via high-resolution differential equations
Shuo Chen, Bin Shi, Ya-xiang Yuan
Nesterov's accelerated gradient descent (NAG) is one of the milestones in the history of first-order algorithms. It was not successfully uncovered until the high-resolution differe…
Proximal Subgradient Norm Minimization of ISTA and FISTA
Bowen Li, Bin Shi, Ya-xiang Yuan
For first-order smooth optimization, the research on the acceleration phenomenon has a long-time history. Until recently, the mechanism leading to acceleration was not successfully…
Gradient Norm Minimization of Nesterov Acceleration:
Shuo Chen, Bin Shi, Ya-xiang Yuan
In the history of first-order algorithms, Nesterov's accelerated gradient descent (NAG) is one of the milestones. However, the cause of the acceleration has been a mystery for a lo…
Generalized truncated moment problems with unbounded sets
Lei Huang, Jiawang Nie, Ya-Xiang Yuan
This paper studies generalized truncated moment problems with unbounded sets. First, we study geometric properties of the truncated moment cone and its dual cone of nonnegative pol…
Homogenization for polynomial optimization with unbounded sets
Lei Huang, Jiawang Nie, Ya-Xiang Yuan
This paper considers polynomial optimization with unbounded sets. We give a homogenization formulation and propose a hierarchy of Moment-SOS relaxations to solve it. Under the assu…
A Penalty-free Infeasible Approach for a Class of Nonsmooth Optimization Problems over the Stiefel Manifold
Nachuan Xiao, Xin Liu, Ya-xiang Yuan
Transforming into an exact penalty function model with convex compact constraints yields efficient infeasible approaches for optimization problems with orthogonality constraints. F…
On the Convergence of Stochastic Gradient Descent with Bandwidth-based Step Size
Xiaoyu Wang, Ya-xiang Yuan
We investigate the stochastic gradient descent (SGD) method where the step size lies within a banded region instead of being given by a fixed formula. The optimal convergence rate…
On the Complexity of an Augmented Lagrangian Method for Nonconvex Optimization
Geovani N. Grapiglia, Ya-xiang Yuan
In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we…
Stochastic Trust Region Methods with Trust Region Radius Depending on Probabilistic Models
Xiaoyu Wang, Ya-xiang Yuan
We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm, termed STRME, in…
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 .…