109 citations · 579 across the 90 of their papers we have counts for
84 papers · 1 filter
Extension on the convergence rates of moment-SOS hierarchies via approximation of truncated moment sequences
Hoang Anh Tran, Kim-Chuan Toh
This paper continues our work on the convergence rates of moment-SOS hierarchies via approximation of truncated moment sequences. We extend the method developed for the Schmüdgen-t…
On the B-subdifferential of proximal operators of affine-constrained regularizer
Xudong Li, Meixia Lin, Kim-Chuan Toh
In this work, we study the affine-constrained regularizers, which frequently arise in statistical and machine learning problems across a variety of applications, including…
On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences
Hoang Anh Tran, Toh Kim-Chuan
The moment-SOS hierarchy is a widely applicable framework to address polynomial optimization problems over basic semi-algebraic sets based on positivity certificates of polynomial.…
NewVEM: A Newton Vertex Exchange Method for a Class of Constrained Self-Concordant Minimization Problems
Ling Liang, Kim-Chuan Toh, Haizhao Yang
We propose \textbf{NewVEM}, a Newton vertex exchange method for efficiently solving self-concordant minimization problems under generalized simplex constraints. The algorithm featu…
Nesterov's Accelerated Jacobi-Type Methods for Large-scale Symmetric Positive Semidefinite Linear Systems
Ling Liang, Qiyuan Pang, Kim-Chuan Toh +1
Solving symmetric positive semidefinite linear systems is an essential task in many scientific computing problems. While Jacobi-type methods, including the classical Jacobi method…
Wasserstein distributionally robust optimization and its tractable regularization formulations
Hong T. M. Chu, Meixia Lin, Kim-Chuan Toh
We study a variety of Wasserstein distributionally robust optimization (WDRO) problems where the distributions in the ambiguity set are chosen by constraining their Wasserstein dis…
An Inexact Halpern Iteration with Application to Distributionally Robust Optimization
Ling Liang, Zusen Xu, Kim-Chuan Toh +1
The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this p…
A feasible method for general convex low-rank SDP problems
Tianyun Tang, Kim-Chuan Toh
In this work, we consider the low rank decomposition (SDPR) of general convex semidefinite programming problems (SDP) that contain both a positive semidefinite matrix and a nonnega…
A Sparse Smoothing Newton Method for Solving Discrete Optimal Transport Problems
Di Hou, Ling Liang, Kim-Chuan Toh
The discrete optimal transport (OT) problem, which offers an effective computational tool for comparing two discrete probability distributions, has recently attracted much attentio…
A Corrected Inexact Proximal Augmented Lagrangian Method with a Relative Error Criterion for a Class of Group-quadratic Regularized Optimal Transport Problems
Lei Yang, Ling Liang, Hong T. M. Chu +1
The optimal transport (OT) problem and its related problems have attracted significant attention and have been extensively studied in various applications. In this paper, we focus…
Self-adaptive ADMM for semi-strongly convex problems
Tianyun Tang, Kim-Chuan Toh
In this paper, we develop a self-adaptive ADMM that updates the penalty parameter adaptively. When one part of the objective function is strongly convex i.e., the problem is semi-s…
On solving a rank regularized minimization problem via equivalent factorized column-sparse regularized models
Wenjing Li, Wei Bian, Kim-Chuan Toh
Rank regularized minimization problem is an ideal model for the low-rank matrix completion/recovery problem. The matrix factorization approach can transform the high-dimensional ra…
Quantifying low rank approximations of third order symmetric tensors
Shenglong Hu, Defeng Sun, Kim-Chuan Toh
In this paper, we present a method to certify the approximation quality of a low rank tensor to a given third order symmetric tensor. Under mild assumptions, best low rank approxim…
Stochastic Subgradient Methods with Guaranteed Global Stability in Nonsmooth Nonconvex Optimization
Nachuan Xiao, Xiaoyin Hu, Kim-Chuan Toh
In this paper, we focus on providing convergence guarantees for stochastic subgradient methods in minimizing nonsmooth nonconvex functions. We first investigate the global stabilit…
A Highly Efficient Algorithm for Solving Exclusive Lasso Problems
Meixia Lin, Yancheng Yuan, Defeng Sun +1
The exclusive lasso (also known as elitist lasso) regularizer has become popular recently due to its superior performance on intra-group feature selection. Its complex nature poses…
Adaptive sieving: A dimension reduction technique for sparse optimization problems
Yancheng Yuan, Meixia Lin, Defeng Sun +1
In this paper, we propose an adaptive sieving (AS) strategy for solving general sparse machine learning models by effectively exploring the intrinsic sparsity of the solutions, whe…
Nonconvex Stochastic Bregman Proximal Gradient Method with Application to Deep Learning
Kuangyu Ding, Jingyang Li, Kim-Chuan Toh
Stochastic gradient methods for minimizing nonconvex composite objective functions typically rely on the Lipschitz smoothness of the differentiable part, but this assumption fails…
Adam-family Methods for Nonsmooth Optimization with Convergence Guarantees
Nachuan Xiao, Xiaoyin Hu, Xin Liu +1
In this paper, we present a comprehensive study on the convergence properties of Adam-family methods for nonsmooth optimization, especially in the training of nonsmooth neural netw…
A Riemannian Dimension-reduced Second Order Method with Application in Sensor Network Localization
Tianyun Tang, Kim-Chuan Toh, Nachuan Xiao +1
In this paper, we propose a cubic-regularized Riemannian optimization method (RDRSOM), which partially exploits the second order information and achieves the iteration complexity o…
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…
On proximal augmented Lagrangian based decomposition methods for dual block-angular convex composite programming problems
Kuang-Yu Ding, Xin-Yee Lam, Kim-Chuan Toh
We design inexact proximal augmented Lagrangian based decomposition methods for convex composite programming problems with dual block-angular structures. Our methods are particular…
A feasible method for solving an SDP relaxation of the quadratic knapsack problem
Tianyun Tang, Kim-Chuan Toh
In this paper, we consider an SDP relaxation of the quadratic knapsack problem (QKP). After using the Burer-Monteiro factorization, we get a non-convex optimization problem, whose…
A squared smoothing Newton method for semidefinite programming
Ling Liang, Defeng Sun, Kim-Chuan Toh
This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properti…
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…