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学者姓名：刘勇进
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Abstract ：
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 等. "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 ：
应用优函数罚方法求解具有低秩密度矩阵约束的最小二乘问题.首先，用凸差方法处理非凸的低秩约束，并结合罚方法和优函数方法将原问题转化为一系列具有密度矩阵约束的凸优化问题；然后，给出求解该优化问题的优函数罚方法，并对该方法进行收敛性分析；最后，运用半光滑牛顿增广拉格朗日算法求解优函数罚方法的子问题.合成数据集和真实数据集上的数值结果表明，优函数罚方法可有效求解具有低秩密度矩阵约束的最小二乘问题.
Keyword ：
优函数罚方法 优函数罚方法 低秩密度矩阵 低秩密度矩阵 最小二乘问题 最小二乘问题
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| GB/T 7714 | 罗曦 , 熊贤祝 , 刘勇进 . 求解低秩密度矩阵约束最小二乘问题的优函数罚方法 [J]. | 福州大学学报(自然科学版) , 2024 , 52 (02) : 127-133 . |
| MLA | 罗曦 等. "求解低秩密度矩阵约束最小二乘问题的优函数罚方法" . | 福州大学学报(自然科学版) 52 . 02 (2024) : 127-133 . |
| APA | 罗曦 , 熊贤祝 , 刘勇进 . 求解低秩密度矩阵约束最小二乘问题的优函数罚方法 . | 福州大学学报(自然科学版) , 2024 , 52 (02) , 127-133 . |
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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 等. "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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重点研究了解决多设施韦伯问题(MFWP)的有效算法。首先，将MFWP重新表述为它的等价形式，然后提出一种半光滑牛顿增广拉格朗日(Ssnal)算法来求解MFWP,并且刻画了Ssnal算法的全局收敛性和局部渐近超线性收敛性。最后，在数据集上进行数值实验，结果表明，Ssnal算法在鲁棒性和计算效率方面都优于双曲近似过程(HAP)算法和交替方向乘子法(ADMM)。
Keyword ：
半光滑牛顿算法 半光滑牛顿算法 增广拉格朗日算法 增广拉格朗日算法 多设施韦伯问题 多设施韦伯问题
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| GB/T 7714 | 杨子斌 , 刘勇进 . 求解多设施韦伯问题的半光滑牛顿增广拉格朗日法 [J]. | 莆田学院学报 , 2023 , 30 (02) : 18-25 . |
| MLA | 杨子斌 等. "求解多设施韦伯问题的半光滑牛顿增广拉格朗日法" . | 莆田学院学报 30 . 02 (2023) : 18-25 . |
| APA | 杨子斌 , 刘勇进 . 求解多设施韦伯问题的半光滑牛顿增广拉格朗日法 . | 莆田学院学报 , 2023 , 30 (02) , 18-25 . |
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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 等. "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 等. "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 等. "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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This paper concerns with efficient projection onto the ordered weighted ℓ1 norm ball, which is equivalent to the problem of finding projector onto the intersection of the monotone nonnegative cone and an affine subspace. Based on Lagrangian relaxation and secant approximation method, we propose an easily implementable yet efficient algorithm to solve the projection problem which is proved to terminate after a finite number of iterations. Furthermore, we design efficient implementations for our algorithm and compare it with a semismooth Newton (Ssn) algorithm and a root-finding (Root-F) algorithm. Numerical results on a diversity of test problems show that our algorithm is superior than Ssn and Root-F. © 2022, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature.
Keyword ：
Lagrangian relaxation Lagrangian relaxation ordered weighted ℓ1 norm ball ordered weighted ℓ1 norm ball secant method secant method
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| GB/T 7714 | Liu, Y.-J. , Xu, J.-J. , Lin, L.-Y. . An Easily Implementable Algorithm for Efficient Projection onto the Ordered Weighted ℓ1 Norm Ball [J]. | Journal of the Operations Research Society of China , 2023 , 11 (4) : 925-940 . |
| MLA | Liu, Y.-J. 等. "An Easily Implementable Algorithm for Efficient Projection onto the Ordered Weighted ℓ1 Norm Ball" . | Journal of the Operations Research Society of China 11 . 4 (2023) : 925-940 . |
| APA | Liu, Y.-J. , Xu, J.-J. , Lin, L.-Y. . An Easily Implementable Algorithm for Efficient Projection onto the Ordered Weighted ℓ1 Norm Ball . | Journal of the Operations Research Society of China , 2023 , 11 (4) , 925-940 . |
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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 等. "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 等. "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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