62 citations · 90 across the 17 of their papers we have counts for
18 papers
A sequential smoothing majorant stochastic approximation method for nonconvex nonconcave minimax problems
Zhouxing Luo, Wei Liu, Xin Liu +1
We propose a sequential smoothing majorant stochastic approximation (SMSA) method for nonconvex-nonconcave minimax optimization problems. To overcome the nonconcavity of the inner…
A Partial Exact Penalty Function Approach for Constrained Optimization
Nachuan Xiao, Xin Liu, Kim-Chuan Toh
In this paper, we focus on a class of constrained nonlinear optimization problems (NLP), where some of its equality constraints define a closed embedded submanifold i…
CDOpt: A Python Package for a Class of Riemannian Optimization
Nachuan Xiao, Xiaoyin Hu, Xin Liu +1
Optimization over the embedded submanifold defined by constraints has attracted much interest over the past few decades due to its wide applications in various areas. Pl…
An Improved Unconstrained Approach for Bilevel Optimization
Xiaoyin Hu, Nachuan Xiao, Xin Liu +1
In this paper, we focus on the nonconvex-strongly-convex bilevel optimization problem (BLO). In this BLO, the objective function of the upper-level problem is nonconvex and possibl…
A Constraint Dissolving Approach for Nonsmooth Optimization over the Stiefel Manifold
Xiaoyin Hu, Nachuan Xiao, Xin Liu +1
This paper focus on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-fr…
Dissolving Constraints for Riemannian Optimization
Nachuan Xiao, Xin Liu, Kim-Chuan Toh
In this paper, we consider optimization problems over closed embedded submanifolds of , which are defined by the constraints . We propose a class of constra…
Solving Optimization Problems over the Stiefel Manifold by Smooth Exact Penalty Function
Nachuan Xiao, Xin Liu
In this paper, we present a novel penalty model called ExPen for optimization over the Stiefel manifold. Different from existing penalty functions for orthogonality constraints, Ex…
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…
Linearly-constrained nonsmooth optimization for training autoencoders
Wei Liu, Xin Liu, Xiaojun Chen
A regularized minimization model with -norm penalty (RP) is introduced for training the autoencoders that belong to a class of two-layer neural networks. We show that the RP c…
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…
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…
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 .…
On the non-ergodic convergence rate of an inexact augmented Lagrangian framework for composite convex programming
Ya-Feng Liu, Xin Liu, Shiqian Ma
In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propo…
On the Analysis of the Discretized Kohn-Sham Density Functional Theory
Xin Liu, Zaiwen Wen, Xiao Wang +2
In this paper, we study a few theoretical issues in the discretized Kohn-Sham (KS) density functional theory (DFT). The equivalence between either a local or global minimizer of th…
Asset Allocation under the Basel Accord Risk Measures
Zaiwen Wen, Xianhua Peng, Xin Liu +2
Financial institutions are currently required to meet more stringent capital requirements than they were before the recent financial crisis; in particular, the capital requirement…
On the Convergence of the Self-Consistent Field Iteration in Kohn-Sham Density Functional Theory
Xin Liu, Xiao Wang, Zaiwen Wen +1
It is well known that the self-consistent field (SCF) iteration for solving the Kohn-Sham (KS) equation often fails to converge, yet there is no clear explanation. In this paper, w…