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学者姓名：刘勇进
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Abstract ：
The generalized convex nearly isotonic regression problem addresses a least squares regression model that incorporates both sparsity and monotonicity constraints on the regression coefficients. In this paper, we introduce an efficient semismooth Newton-based augmented Lagrangian (Ssnal) algorithm to solve this problem. We demonstrate that, under reasonable assumptions, the Ssnal algorithm achieves global convergence and exhibits a linear convergence rate. Computationally, we derive the generalized Jacobian matrix associated with the proximal mapping of the generalized convex nearly isotonic regression regularizer and leverage the second-order sparsity when applying the semismooth Newton method to the subproblems in the Ssnal algorithm. Numerical experiments conducted on both synthetic and real datasets clearly demonstrate that our algorithm significantly outperforms first-order methods in terms of efficiency and robustness.
Keyword ：
augmented Lagrangian algorithm augmented Lagrangian algorithm generalized convex nearly isotonic regression generalized convex nearly isotonic regression semismooth Newton method semismooth Newton method
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| GB/T 7714 | Xu, Yanmei , Lin, Lanyu , Liu, Yong-Jin . A Semismooth Newton-Based Augmented Lagrangian Algorithm for the Generalized Convex Nearly Isotonic Regression Problem [J]. | MATHEMATICS , 2025 , 13 (3) . |
| MLA | Xu, Yanmei 等. "A Semismooth Newton-Based Augmented Lagrangian Algorithm for the Generalized Convex Nearly Isotonic Regression Problem" . | MATHEMATICS 13 . 3 (2025) . |
| APA | Xu, Yanmei , Lin, Lanyu , Liu, Yong-Jin . A Semismooth Newton-Based Augmented Lagrangian Algorithm for the Generalized Convex Nearly Isotonic Regression Problem . | MATHEMATICS , 2025 , 13 (3) . |
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Nonconvex minimax problems frequently arise in machine learning, distributionally robust optimization, and many other research fields. In this paper, we propose a Stochastic Alternating Mirror Descent Ascent with Momentum (SAMDAM) algorithm to solve nonconvex-strongly concave minimax optimization problems. SAMDAM employs simple mirror descent ascent steps along with momentum acceleration to update the variables \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y$$\end{document} alternately at each iteration. We further prove that SAMDAM achieves a gradient complexity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{O}(\kappa<^>{3}\epsilon<^>{-4})$$\end{document} for finding an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon$$\end{document}-stationary point in stochastic nonconvex settings, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa$$\end{document} represents the condition number of the problem. Finally, computational experiments demonstrate that SAMDAM outperforms several state-of-the-art algorithms in distributionally robust optimization and fair classification tasks.
Keyword ：
Complexity Complexity Machine learning Machine learning Nonconvex minimax optimization problem Nonconvex minimax optimization problem Stochastic alternating mirror descent ascent with momentum algorithm Stochastic alternating mirror descent ascent with momentum algorithm
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| GB/T 7714 | Zhao, Lulu , Liu, Yue , Liu, Yong-Jin . Accelerated stochastic alternating mirror descent ascent algorithm for nonconvex-strongly concave minimax problems [J]. | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING , 2025 . |
| MLA | Zhao, Lulu 等. "Accelerated stochastic alternating mirror descent ascent algorithm for nonconvex-strongly concave minimax problems" . | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING (2025) . |
| APA | Zhao, Lulu , Liu, Yue , Liu, Yong-Jin . Accelerated stochastic alternating mirror descent ascent algorithm for nonconvex-strongly concave minimax problems . | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING , 2025 . |
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Lov & aacute;sz theta SDP problem can often be regarded as semidefinite programming (SDP) relaxation of combinatorial optimization problems in graph theory and appears in various fields. In this paper, we study a semismooth Newton based augmented Lagrangian (Ssnal) algorithm for solving Lov & aacute;sz theta SDP problem. There are three major ingredients in this paper. Firstly, we design efficient implementations of the Ssnal algorithm for solving dual problem of Lov & aacute;sz theta SDP problem. Secondly, the global convergence and local asymptotic superlinear convergence of the Ssnal algorithm are characterized under very mild conditions, in which a semismooth Newton (Ssn) method with superlinear or even quadratic convergence is applied to solve the subproblem. Finally, numerical experiments conducted on random and real data sets demonstrate that the Ssnal algorithm outperforms Sdpnal+ solver. In particular, the Ssnal algorithm can efficiently solve large-scale Lov & aacute;sz theta SDP problems with high accuracy, where the matrix dimension is up to 3000 and the number of equality constraints is up to 27,484.
Keyword ：
augmented Lagrangian method augmented Lagrangian method Lov & aacute;sz theta SDP problem Lov & aacute;sz theta SDP problem semidefinite programming semidefinite programming semismooth Newton method semismooth Newton method
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| GB/T 7714 | Chen, Suyu , Liu, Yong-Jin , Yu, Jing et al. A semismooth Newton based augmented Lagrangian algorithm for Lovász theta SDP problem [J]. | OPTIMIZATION , 2025 . |
| MLA | Chen, Suyu et al. "A semismooth Newton based augmented Lagrangian algorithm for Lovász theta SDP problem" . | OPTIMIZATION (2025) . |
| APA | Chen, Suyu , Liu, Yong-Jin , Yu, Jing , Zhou, Weimi . A semismooth Newton based augmented Lagrangian algorithm for Lovász theta SDP problem . | OPTIMIZATION , 2025 . |
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Motivation The classification task based on whole-slide images (WSIs) is a classic problem in computational pathology. Multiple instance learning (MIL) provides a robust framework for analyzing whole slide images with slide-level labels at gigapixel resolution. However, existing MIL models typically focus on modeling the relationships between instances while neglecting the variability across the channel dimensions of instances, which prevents the model from fully capturing critical information in the channel dimension.Results To address this issue, we propose a plug-and-play module called Multi-scale Channel Attention Block (MCAB), which models the interdependencies between channels by leveraging local features with different receptive fields. By alternately stacking four layers of Transformer and MCAB, we designed a channel attention-based MIL model (CAMIL) capable of simultaneously modeling both inter-instance relationships and intra-channel dependencies. To verify the performance of the proposed CAMIL in classification tasks, several comprehensive experiments were conducted across three datasets: Camelyon16, TCGA-NSCLC, and TCGA-RCC. Empirical results demonstrate that, whether the feature extractor is pretrained on natural images or on WSIs, our CAMIL surpasses current state-of-the-art MIL models across multiple evaluation metrics.Availability and implementation All implementation code is available at https://github.com/maojy0914/CAMIL.
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| GB/T 7714 | Mao, Jinyang , Xu, Junlin , Tang, Xianfang et al. CAMIL: channel attention-based multiple instance learning for whole slide image classification [J]. | BIOINFORMATICS , 2025 , 41 (2) . |
| MLA | Mao, Jinyang et al. "CAMIL: channel attention-based multiple instance learning for whole slide image classification" . | BIOINFORMATICS 41 . 2 (2025) . |
| APA | Mao, Jinyang , Xu, Junlin , Tang, Xianfang , Liu, Yongjin , Zhao, Heaven , Tian, Geng et al. CAMIL: channel attention-based multiple instance learning for whole slide image classification . | BIOINFORMATICS , 2025 , 41 (2) . |
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Abstract ：
我们考虑在高维环境下的二分类问题,其中给定数据的特征数大于观测数.为此,我们提出一种基于依附惩罚的最优评分(APOS)模型,用于同时进行判别分析和特征选择.在本文中,我们设计一种基于块坐标下降(BCD)方法和SSNAL算法的高效算法来近似求解APOS模型,并给出该方法的收敛性结果.对模拟和真实数据集的数值实验结果表明,所提模型在性能上优于五种经典的稀疏判别方法.
Keyword ：
BCD方法 BCD方法 SSNAL算法 SSNAL算法 最优评分 最优评分 特征选择 特征选择 稀疏判别分析 稀疏判别分析
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| GB/T 7714 | 侯丹丹 , 刘勇进 . 基于依附惩罚的稀疏最优评分模型 [J]. | 数学理论与应用 , 2024 , 44 (4) : 100-115 . |
| MLA | 侯丹丹 et al. "基于依附惩罚的稀疏最优评分模型" . | 数学理论与应用 44 . 4 (2024) : 100-115 . |
| APA | 侯丹丹 , 刘勇进 . 基于依附惩罚的稀疏最优评分模型 . | 数学理论与应用 , 2024 , 44 (4) , 100-115 . |
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The Fantope-constrained sparse principal subspace estimation problem is initially proposed Vu et al. (Vu et al., 2013). This paper investigates a semismooth Newton based proximal point (P PASSN ) algorithm for solving the equivalent form of this problem, where a semismooth Newton (S SN ) method is utilized to optimize the inner problems involved in the P PASSN algorithm. Under standard conditions, the P PASSN algorithm is proven to achieve global convergence and asymptotic superlinear convergence rate. Computationally, we derive nontrivial expressions the Fantope projection and its generalized Jacobian, which are key ingredients for the P PASSN algorithm. Some numerical results on synthetic and real data sets are presented to illustrate the effectiveness of the proposed P PASSN algorithm for large-scale problems and superiority over the alternating direction method of multipliers (ADMM).
Keyword ：
Fantope projection Fantope projection Generalized Jacobian Generalized Jacobian Proximal point algorithm Proximal point algorithm Semismooth Newton algorithm Semismooth Newton algorithm
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| GB/T 7714 | Liu, Yong-Jin , Wan, Yuqi , Lin, Lanyu . An efficient algorithm for Fantope-constrained sparse principal subspace estimation problem [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2024 , 475 . |
| MLA | Liu, Yong-Jin et al. "An efficient algorithm for Fantope-constrained sparse principal subspace estimation problem" . | APPLIED MATHEMATICS AND COMPUTATION 475 (2024) . |
| APA | Liu, Yong-Jin , Wan, Yuqi , Lin, Lanyu . An efficient algorithm for Fantope-constrained sparse principal subspace estimation problem . | APPLIED MATHEMATICS AND COMPUTATION , 2024 , 475 . |
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Abstract ：
我们考虑在高维环境下的二分类问题,其中给定数据的特征数大于观测数.为此,我们提出一种基于依附惩罚的最优评分(APOS)模型,用于同时进行判别分析和特征选择.在本文中,我们设计一种基于块坐标下降(BCD)方法和SSNAL算法的高效算法来近似求解APOS模型,并给出该方法的收敛性结果.对模拟和真实数据集的数值实验结果表明,所提模型在性能上优于五种经典的稀疏判别方法.
Keyword ：
BCD方法 BCD方法 SSNAL算法 SSNAL算法 最优评分 最优评分 特征选择 特征选择 稀疏判别分析 稀疏判别分析
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| GB/T 7714 | 侯丹丹 , 刘勇进 . 基于依附惩罚的稀疏最优评分模型（英文） [J]. | 数学理论与应用 , 2024 , 44 (04) : 100-115 . |
| MLA | 侯丹丹 et al. "基于依附惩罚的稀疏最优评分模型（英文）" . | 数学理论与应用 44 . 04 (2024) : 100-115 . |
| APA | 侯丹丹 , 刘勇进 . 基于依附惩罚的稀疏最优评分模型（英文） . | 数学理论与应用 , 2024 , 44 (04) , 100-115 . |
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This paper is concerned with the l(1),infinity-norm ball constrained multi-task learning problem, which has received extensive attention in many research areas such as machine learning, cognitive neuroscience, and signal processing. To address the challenges of solving large-scale multi-task Lasso problems, this paper develops an inexact semismooth Newton-based augmented Lagrangian (Ssnal) algorithm. When solving the inner problems in the Ssnal algorithm, the semismooth Newton (Ssn) algorithm with superlinear or even quadratic convergence is applied. Theoretically, this paper presents the global and asymptotically superlinear local convergence of the Ssnal algorithm under standard conditions. Computationally, we derive an efficient procedure to construct the generalized Jacobian of the projector onto l(1),infinity-norm ball, which is an important component of the Ssnal algorithm, making the computational cost in the Ssn algorithm very cheap. Comprehensive numerical experiments on the multi-task Lasso problems demonstrate that the Ssnal algorithm is more efficient and robust than several existing state-of-the-art first-order algorithms.
Keyword ：
augmented Lagrangian algorithm augmented Lagrangian algorithm generalized Jacobian generalized Jacobian Multi-task Lasso problem Multi-task Lasso problem semismooth Newton algorithm semismooth Newton algorithm
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| GB/T 7714 | Lin, Lanyu , Liu, Yong-Jin . An Inexact Semismooth Newton-Based Augmented Lagrangian Algorithm for Multi-Task Lasso Problems [J]. | ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH , 2023 , 41 (03) . |
| MLA | Lin, Lanyu et al. "An Inexact Semismooth Newton-Based Augmented Lagrangian Algorithm for Multi-Task Lasso Problems" . | ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 41 . 03 (2023) . |
| APA | Lin, Lanyu , Liu, Yong-Jin . An Inexact Semismooth Newton-Based Augmented Lagrangian Algorithm for Multi-Task Lasso Problems . | ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH , 2023 , 41 (03) . |
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研究超平面交单调锥上的投影问题,给出求解该问题的池相邻违反算法和半光滑牛顿法,并对算法进行有效性分析,最后将两种算法进行数值对比.数值实验结果表明:在求解随机数据集上的投影问题时,池相邻违反算法比目前流行的半光滑牛顿算法更高效.
Keyword ：
半光滑牛顿法 半光滑牛顿法 投影算子 投影算子 池相邻违反算法 池相邻违反算法 超平面交单调锥 超平面交单调锥
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| GB/T 7714 | 刘勇进 , 汤婉红 . 超平面交单调锥上投影算子的快速算法及其实现 [J]. | 福州大学学报（自然科学版） , 2023 , 51 (3) : 293-300 . |
| MLA | 刘勇进 et al. "超平面交单调锥上投影算子的快速算法及其实现" . | 福州大学学报（自然科学版） 51 . 3 (2023) : 293-300 . |
| APA | 刘勇进 , 汤婉红 . 超平面交单调锥上投影算子的快速算法及其实现 . | 福州大学学报（自然科学版） , 2023 , 51 (3) , 293-300 . |
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The maximum eigenvalue problem is to minimize the maximum eigenvalue function over an affine subspace in a symmetric matrix space, which has many applications in structural engineering, such as combinatorial optimization, control theory and structural design. Based on classical analysis of proximal point (Ppa) algorithm and semismooth analysis of nonseparable spectral operator, we propose an efficient semismooth Newton based dual proximal point (Ssndppa) algorithm to solve the maximum eigenvalue problem, in which an inexact semismooth Newton (Ssn) algorithm is applied to solve inner subproblem of the dual proximal point (d-Ppa) algorithm. Global convergence and locally asymptotically superlinear convergence of the d-Ppa algorithm are established under very mild conditions, and fast superlinear or even quadratic convergence of the Ssn algorithm is obtained when the primal constraint nondegeneracy condition holds for the inner subproblem. Computational costs of the Ssn algorithm for solving the inner subproblem can be reduced by fully exploiting low-rank or high-rank property of a matrix. Numerical experiments on max-cut problems and randomly generated maximum eigenvalue optimization problems demonstrate that the Ssndppa algorithm substantially outperforms the Sdpnal+ solver and several state-of-the-art first-order algorithms.
Keyword ：
Density matrix Density matrix Maximum eigenvalue problem Maximum eigenvalue problem Proximal point algorithm Proximal point algorithm Quadratic growth condition Quadratic growth condition Semismooth Newton algorithm Semismooth Newton algorithm
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| GB/T 7714 | Liu, Yong-Jin , Yu, Jing . A semismooth Newton based dual proximal point algorithm for maximum eigenvalue problem [J]. | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS , 2023 , 85 (2) : 547-582 . |
| MLA | Liu, Yong-Jin et al. "A semismooth Newton based dual proximal point algorithm for maximum eigenvalue problem" . | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 85 . 2 (2023) : 547-582 . |
| APA | Liu, Yong-Jin , Yu, Jing . A semismooth Newton based dual proximal point algorithm for maximum eigenvalue problem . | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS , 2023 , 85 (2) , 547-582 . |
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