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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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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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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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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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This paper investigates a semismooth Newton based augmented Lagrangian (SSNAL) algorithm for solving equivalent formulation of the general l(1) trend filtering problem. The computational costs of a semismooth Newton (SSN) algorithm for solving the subproblem in the SSNAL algorithm can be substantially reduced by exploiting the second order sparsity of Hessian matrix and some efficient techniques. The global convergence and the asymptotically superlinear local convergence of the SSNAL algorithm are given under mild conditions. Numerical comparisons between the SSNAL algorithm and other state-of-the-art algorithms on real and synthetic data sets validate that our algorithm has superior performance in both robustness and efficiency.
Keyword ：
augmented Lagrangian algorithm augmented Lagrangian algorithm general l(1) trend filtering general l(1) trend filtering semismooth Newton algorithm semismooth Newton algorithm sparse Hessian sparse Hessian
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| GB/T 7714 | Liut, Yong-jin , Zhang, Tiqi . SPARSE HESSIAN BASED SEMISMOOTH NEWTON AUGMENTED LAGRANGIAN ALGORITHM FOR GENERAL l(1) TREND FILTERING [J]. | PACIFIC JOURNAL OF OPTIMIZATION , 2023 , 19 (2) : 187-204 . |
| MLA | Liut, Yong-jin et al. "SPARSE HESSIAN BASED SEMISMOOTH NEWTON AUGMENTED LAGRANGIAN ALGORITHM FOR GENERAL l(1) TREND FILTERING" . | PACIFIC JOURNAL OF OPTIMIZATION 19 . 2 (2023) : 187-204 . |
| APA | Liut, Yong-jin , Zhang, Tiqi . SPARSE HESSIAN BASED SEMISMOOTH NEWTON AUGMENTED LAGRANGIAN ALGORITHM FOR GENERAL l(1) TREND FILTERING . | PACIFIC JOURNAL OF OPTIMIZATION , 2023 , 19 (2) , 187-204 . |
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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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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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This paper is concerned with efficient algorithms for solving Weber problem, which is an important problem arising in the facility location problems. In this paper, we reformulate the Weber problem as its equivalent form and then propose a semismooth Newton based augmented Lagrangian (SSNAL) algorithm for solving Weber problem. The global convergence and locally asymptotically superlinear convergence of the SSNAL algorithm are characterized under mild conditions. Numerical experiments conducted on synthetic data sets demonstrate that the SSNAL algorithm outperforms several state-of-the-art algorithms in terms of efficiency and robustness.
Keyword ：
augmented Lagrangian algorithm augmented Lagrangian algorithm semismooth Newton method semismooth Newton method Weber problem Weber problem
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| GB/T 7714 | Liu, Yong Jin , Zhu, Qinxin . A SEMISMOOTH NEWTON BASED AUGMENTED LAGRANGIAN ALGORITHM FOR WEBER PROBLEM [J]. | PACIFIC JOURNAL OF OPTIMIZATION , 2022 , 18 (2) : 299-315 . |
| MLA | Liu, Yong Jin et al. "A SEMISMOOTH NEWTON BASED AUGMENTED LAGRANGIAN ALGORITHM FOR WEBER PROBLEM" . | PACIFIC JOURNAL OF OPTIMIZATION 18 . 2 (2022) : 299-315 . |
| APA | Liu, Yong Jin , Zhu, Qinxin . A SEMISMOOTH NEWTON BASED AUGMENTED LAGRANGIAN ALGORITHM FOR WEBER PROBLEM . | PACIFIC JOURNAL OF OPTIMIZATION , 2022 , 18 (2) , 299-315 . |
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The density matrix least squares problem arises from the quantum state tomography problem in experimental physics and has many applications in signal processing and machine learning, mainly including the phase recovery problem and the matrix completion problem. In this paper, we first reformulate the density matrix least squares problem as an equivalent convex optimization problem and then design an efficient semismooth Newton-based augmented Lagrangian (Ssnal) algorithm to solve the dual of its equivalent form, in which an inexact semismooth Newton (Ssn) algorithm with superlinear or even quadratic convergence is applied to solve the inner subproblems. Theoretically, the global convergence and locally asymptotically superlinear convergence of the Ssnal algorithm are established under very mild conditions. Computationally, the costs of the Ssn algorithm for solving the subproblem are significantly reduced by making full use of low-rank or high-rank property of optimal solutions of the density matrix least squares problem. In order to verify the performance of our algorithm, numerical experiments conducted on randomly generated quantum state tomography problems and density matrix least squares problems with real data demonstrate that the Ssnal algorithm is more effective and robust than the Qsdpnal solver and several state-of-the-art first-order algorithms.
Keyword ：
Augmented Lagrangian algorithm Augmented Lagrangian algorithm Density matrix least squares problems Density matrix least squares problems 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 Augmented Lagrangian Algorithm for Density Matrix Least Squares Problems [J]. | JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS , 2022 , 195 (3) : 749-779 . |
| MLA | Liu, Yong-Jin et al. "A Semismooth Newton-based Augmented Lagrangian Algorithm for Density Matrix Least Squares Problems" . | JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 195 . 3 (2022) : 749-779 . |
| APA | Liu, Yong-Jin , Yu, Jing . A Semismooth Newton-based Augmented Lagrangian Algorithm for Density Matrix Least Squares Problems . | JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS , 2022 , 195 (3) , 749-779 . |
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This paper focuses on efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian. Based on the Lagrangian duality theory, we deal with the projection problem via a semismooth Newton algorithm with line search safeguard, which admits global and locally quadratic convergence, to solve a univariate semismooth equation. Numerical experiments show that our proposed algorithm outperforms favourably the existing state-of-the-art standard solvers and is able to reliably solve very large-scale projection problems. Besides, we derive an explicit expression of a generalized Jacobian of the studied projection, which is an essential component of second-order nonsmooth methods.
Keyword ：
generalized Jacobian generalized Jacobian Projection Projection semismooth Newton method semismooth Newton method
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| GB/T 7714 | Wang, Bo , Lin, Lanyu , Liu, Yong-Jin . Efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian [J]. | OPTIMIZATION , 2021 , 71 (4) : 1073-1096 . |
| MLA | Wang, Bo et al. "Efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian" . | OPTIMIZATION 71 . 4 (2021) : 1073-1096 . |
| APA | Wang, Bo , Lin, Lanyu , Liu, Yong-Jin . Efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian . | OPTIMIZATION , 2021 , 71 (4) , 1073-1096 . |
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