26 citations · 51 across the 21 of their papers we have counts for
21 papers
Optimality Conditions and Numerical Algorithms for A Class of Linearly Constrained Minimax Optimization Problems
Yu-Hong Dai, Jiani Wang, Liwei Zhang
It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint linear constr…
The Augmented Lagrangian Method Can Approximately Solve Convex Optimization with Least Constraint Violation
Yu-Hong Dai, Liwei Zhang
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constra…
Stability for Constrained Minimax Optimization
Yu-Hong Dai, Liwei Zhang
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stabili…
Convergent and orthogonality preserving schemes for approximating the Kohn-Sham orbitals
Xiaoying Dai, Liwei Zhang, Aihui Zhou
To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure calculations. In this paper, we propose…
Majorized Semi-proximal Alternating Coordinate Method for Nonsmooth Convex-Concave Minimax Optimization
Yu-Hong Dai, Jiani Wang, Liwei Zhang
Minimax optimization problems are an important class of optimization problems arising from modern machine learning and traditional research areas. While there have been many numeri…
Optimization with Least Constraint Violation
Yu-Hong Dai, Liwei Zhang
Study about theory and algorithms for constrained optimization usually assumes that the feasible region of the optimization problem is nonempty. However, there are many important p…
Statistical Robustness of Empirical Risks in Machine Learning
Shaoyan Guo, Huifu Xu, Liwei Zhang
This paper studies convergence of empirical risks in reproducing kernel Hilbert spaces (RKHS). A conventional assumption in the existing research is that empirical training data do…
Optimality Conditions for Constrained Minimax Optimization
Yu-HOng Dai, Liwei Zhang
Minimax optimization problems arises from both modern machine learning including generative adversarial networks, adversarial training and multi-agent reinforcement learning, as we…
Pactical Newton Methods for Electronic Structure Calculations
Xiaoying Dai, Liwei Zhang, Aihui Zhou
In this paper, we propose and analyze some practical Newton methods for electronic structure calculations. We show the convergence and the local quadratic convergence rate for the…
Stochastic Approximation Proximal Method of Multipliers for Convex Stochastic Programming
Liwei Zhang, Yule Zhang, Jia Wu
This paper considers the problem of minimizing a convex expectation function over a closed convex set, coupled with a set of inequality convex expectation constraints. We present a…
Adaptive Step Size Strategy for Orthogonality Constrained Line Search Methods
Xiaoying Dai, Liwei Zhang, Aihui Zhou
In this paper, we propose an adaptive step size strategy for a class of line search methods for orthogonality constrained minimization problems, which avoids the classic backtracki…
Online Alternating Direction Method of Multipliers for Online Composite Optimization
Yule Zhang, Zehao Xiao, Jia Wu +1
In this paper, we investigate regrets of an online semi-proximal alternating direction method of multiplier (Online-spADMM) for solving online linearly constrained convex composite…
Critical Multipliers in Semidefinite Programming
Tianyu Zhang, Liwei Zhang
It was proved in [14] that the existence of a noncritical multiplier for a (smooth) nonlinear programming problem is equivalent to an error bound condition for the Karush-Kuhn-Thck…
Continuous Behavioural Function Equilibria and Approximation Schemes in Bayesian Games with Non-Finite Type and Action Spaces
Shaoyan Guo, Huifu Xu, Liwei Zhang
Meirowitz [17] showed existence of continuous behavioural function equilibria for Bayesian games with non-finite type and action spaces. A key condition for the proof of the existe…
The Rate of Convergence of the Augmented Lagrangian Method for a Nonlinear Semidefinite Nuclear Norm Composite Optimization Problem
Liwei Zhang, Yule Zhang, Jia Wu
We propose two basic assumptions, under which the rate of convergence of the augmented Lagrange method for a class of composite optimization problems is estimated. We analyze the r…
A Linearly Convergent Majorized ADMM with Indefinite Proximal Terms for Convex Composite Programming and Its Applications
Ning Zhang, Jia Wu, Liwei Zhang
This paper aims to study a majorized alternating direction method of multipliers with indefinite proximal terms (iPADMM) for convex composite optimization problems. We show that th…
A Regularized Semi-Smooth Newton Method With Projection Steps for Composite Convex Programs
Xiantao Xiao, Yongfeng Li, Zaiwen Wen +1
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many w…
A conjugate gradient method for electronic structure calculations
Xiaoying Dai, Zhuang Liu, Liwei Zhang +1
In this paper, we study a conjugate gradient method for electronic structure calculations. We propose a Hessian based step size strategy, which together with three orthogonality ap…
Characterization of the Robust Isolated Calmness for a Class of Conic Programming Problems
Chao Ding, Defeng Sun, Liwei Zhang
This paper is devoted to studying the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) solution mapping for a large class of interesting conic programming problems (includi…
Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Quadratic and Semi-Definite Programming
Deren Han, Defeng Sun, Liwei Zhang
In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained…
Smoothing SQP methods for solving degenerate nonsmooth constrained optimization problems with applications to bilevel programs
Mengwei Xu, Jane Ye, Liwei Zhang
We consider a degenerate nonsmooth and nonconvex optimization problem for which the standard constraint qualification such as the generalized Mangasarian Fromovitz constraint quali…