2 citations · 2 across the 15 of their papers we have counts for
17 papers
An Inexact Halpern-accelerated Preconditioned Generalized Proximal Point Algorithm for the Maximal Monotone Inclusion Problem
Lei Yang, Haihang Lan, Di Hou +2
This paper studies an inexact Halpern-accelerated generalized proximal point algorithm with an admissible positive semidefinite preconditioner for solving maximal mon…
Robust principal component analysis with rank and cardinality regularization under matrix factorization
Wenjing Li, Wei Bian, Kim-Chuan Toh
Robust principal component analysis is an important representative method in data analysis. It is usually viewed as an optimization problem involving the rank and -norm of…
On the efficient computation of proximal operators of affine-constrained nonconvex functions
Di Hou, Tianyun Tang, Kim-Chuan Toh +1
Proximal operators with affine constraints arise in numerous models in nonconvex projection, composite optimization, and structured regularization. However, their efficient computa…
Partial Envelope for Optimization Problem with Nonconvex Constraints
Xiaoyin Hu, Xin Liu, Kim-Chuan Toh +1
In this paper, we consider the nonlinear constrained optimization problem (NCP) with constraint set , where is a closed convex subset…
Convergence Analysis of a Relative-type Inexact Preconditioned Proximal ALM for Convex Nonlinear Programming
Lei Yang, Jiayi Zhu, Ling Liang +1
This article investigates the convergence properties of a relative-type inexact preconditioned proximal augmented Lagrangian method (ripALM) for convex nonlinear programming, a…
Improved Rates for Stochastic Variance-Reduced Difference-of-Convex Algorithms
Anh Duc Nguyen, Alp Yurtsever, Suvrit Sra +1
In this work, we propose and analyze DCA-PAGE, a novel algorithm that integrates the difference-of-convex algorithm (DCA) with the ProbAbilistic Gradient Estimator (PAGE) to solve…
On exploration of an interior mirror descent flow for stochastic nonconvex constrained problem
Kuangyu Ding, Kim-Chuan Toh
We study a nonsmooth nonconvex optimization problem defined over nonconvex constraints, where the feasible set is given by the intersection of the closure of an open set and a smoo…
A Hybrid Subgradient Method for Nonsmooth Nonconvex Bilevel Optimization
Nachuan Xiao, Xiaoyin Hu, Xin Liu +1
In this paper, we focus on the nonconvex-nonconvex bilevel optimization problem (BLO), where both upper-level and lower-level objectives are nonconvex, with the upper-level problem…
ripALM: A Relative-Type Inexact Proximal Augmented Lagrangian Method for Linearly Constrained Convex Optimization
Jiayi Zhu, Ling Liang, Lei Yang +1
Inexact proximal augmented Lagrangian methods (ipALMs) have been widely used for solving linearly constrained convex optimization problems, owing to their strong theoretical guaran…
A Minimization Approach for Minimax Optimization with Coupled Constraints
Xiaoyin Hu, Kim-Chuan Toh, Shiwei Wang +1
In this paper, we focus on the nonconvex-strongly-concave minimax optimization problem (MCC), where the inner maximization subproblem contains constraints that couple the primal va…
Learning-rate-free Momentum SGD with Reshuffling Converges in Nonsmooth Nonconvex Optimization
Xiaoyin Hu, Nachuan Xiao, Xin Liu +1
In this paper, we propose a generalized framework for developing learning-rate-free momentum stochastic gradient descent (SGD) methods in the minimization of nonsmooth nonconvex fu…
An Inexact Bregman Proximal Difference-of-Convex Algorithm with Two Types of Relative Stopping Criteria
Lei Yang, Jingjing Hu, Kim-Chuan Toh
In this paper, we consider a class of difference-of-convex (DC) optimization problems, which require only a weaker restricted -smooth adaptable property on the smooth part of th…
Developing Lagrangian-based Methods for Nonsmooth Nonconvex Optimization
Nachuan Xiao, Kuangyu Ding, Xiaoyin Hu +1
In this paper, we consider the minimization of a nonsmooth nonconvex objective function over a closed convex subset of , with additional nonsmoot…
Stochastic Bregman Subgradient Methods for Nonsmooth Nonconvex Optimization Problems
Kuangyu Ding, Kim-Chuan Toh
This paper focuses on the problem of minimizing a locally Lipschitz continuous function. Motivated by the effectiveness of Bregman gradient methods in training nonsmooth deep neura…
On Partial Optimal Transport: Revising the Infeasibility of Sinkhorn and Efficient Gradient Methods
Anh Duc Nguyen, Tuan Dung Nguyen, Quang Minh Nguyen +3
This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most supports and its applications in various AI tasks such as color tran…
Adam-family Methods with Decoupled Weight Decay in Deep Learning
Kuangyu Ding, Nachuan Xiao, Kim-Chuan Toh
In this paper, we investigate the convergence properties of a wide class of Adam-family methods for minimizing quadratically regularized nonsmooth nonconvex optimization problems,…
Inexact Bregman Proximal Gradient Method and its Inertial Variant with Absolute and Partial Relative Stopping Criteria
Lei Yang, Kim-Chuan Toh
The Bregman proximal gradient method (BPGM), which uses the Bregman distance as a proximity measure in the iterative scheme, has recently been re-developed for minimizing convex co…