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学者姓名：张海斌
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摘要 ：
Privacy-preserving empirical risk minimization model is crucial for the increasingly frequent setting of analyzing personal data, such as medical records, financial records, etc. Due to its advantage of a rigorous mathematical definition, differential privacy has been widely used in privacy protection and has received much attention in recent years of privacy protection. With the advantages of iterative algorithms in solving a variety of problems, like empirical risk minimization, there have been various works in the literature that target differentially private iteration algorithms, especially the adaptive iterative algorithm. However, the solution of the final model parameters is imprecise because of the vast privacy budget spending on the step size search. In this paper, we first proposed a novel adaptive differential privacy algorithm that does not require the privacy budget for step size determination. Then, through the theoretical analyses, we prove that our proposed algorithm satisfies differential privacy, and their solutions achieve sufficient accuracy by infinite steps. Furthermore, numerical analysis is performed based on real-world databases. The results indicate that our proposed algorithm outperforms existing algorithms for model fitting in terms of accuracy.
关键词 ：
iteration algorithm iteration algorithm empirical risk minimization empirical risk minimization Differential privacy Differential privacy
引用：
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| GB/T 7714 | Zhang, Kaili , Zhang, Haibin , Zhao, Pengfei et al. A Novel Adaptive Differential Privacy Algorithm for Empirical Risk Minimization [J]. | ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH , 2021 , 38 (05) . |
| MLA | Zhang, Kaili et al. "A Novel Adaptive Differential Privacy Algorithm for Empirical Risk Minimization" . | ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 38 . 05 (2021) . |
| APA | Zhang, Kaili , Zhang, Haibin , Zhao, Pengfei , Chen, Haibin . A Novel Adaptive Differential Privacy Algorithm for Empirical Risk Minimization . | ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH , 2021 , 38 (05) . |
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引用：
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| GB/T 7714 | Bai, Bofeng , Zhang, Haibin , Cheng, Lixin et al. Selected Papers from the 1st International Symposium on Thermal-Fluid Dynamics (ISTFD2019) [J]. | HEAT TRANSFER ENGINEERING , 2021 . |
| MLA | Bai, Bofeng et al. "Selected Papers from the 1st International Symposium on Thermal-Fluid Dynamics (ISTFD2019)" . | HEAT TRANSFER ENGINEERING (2021) . |
| APA | Bai, Bofeng , Zhang, Haibin , Cheng, Lixin , Ghajar, Afshin J. . Selected Papers from the 1st International Symposium on Thermal-Fluid Dynamics (ISTFD2019) . | HEAT TRANSFER ENGINEERING , 2021 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In the fields of wireless communication and data processing, there are varieties of mathematical optimization problems, especially nonconvex and nonsmooth problems. For these problems, one of the biggest difficulties is how to improve the speed of solution. To this end, here we mainly focused on a minimization optimization model that is nonconvex and nonsmooth. Firstly, an inertial Douglas-Rachford splitting (IDRS) algorithm was established, which incorporate the inertial technology into the framework of the Douglas-Rachford splitting algorithm. Then, we illustrated the iteration sequence generated by the proposed IDRS algorithm converges to a stationary point of the nonconvex nonsmooth optimization problem with the aid of the Kurdyka-Lojasiewicz property. Finally, a series of numerical experiments were carried out to prove the effectiveness of our proposed algorithm from the perspective of signal recovery. The results are implicit that the proposed IDRS algorithm outperforms another algorithm.
关键词 ：
Douglas-Rachford splitting Douglas-Rachford splitting inertial inertial Kurdyka-Lojasiewicz property Kurdyka-Lojasiewicz property nonconvex and nonsmooth optimization nonconvex and nonsmooth optimization
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| GB/T 7714 | Feng, Junkai , Zhang, Haibin , Zhang, Kaili et al. An inertial Douglas-Rachford splitting algorithm for nonconvex and nonsmooth problems [J]. | CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE , 2021 . |
| MLA | Feng, Junkai et al. "An inertial Douglas-Rachford splitting algorithm for nonconvex and nonsmooth problems" . | CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE (2021) . |
| APA | Feng, Junkai , Zhang, Haibin , Zhang, Kaili , Zhao, Pengfei . An inertial Douglas-Rachford splitting algorithm for nonconvex and nonsmooth problems . | CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE , 2021 . |
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| GB/T 7714 | Zhang, Yuqi , Zhang, Haibin , Tian, Yingjie . Sparse multiple instance learning with non -convex penalty [J]. | NEUROCOMPUTING , 2020 , 391 : 142-156 . |
| MLA | Zhang, Yuqi et al. "Sparse multiple instance learning with non -convex penalty" . | NEUROCOMPUTING 391 (2020) : 142-156 . |
| APA | Zhang, Yuqi , Zhang, Haibin , Tian, Yingjie . Sparse multiple instance learning with non -convex penalty . | NEUROCOMPUTING , 2020 , 391 , 142-156 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
This work analyzes the alternating minimization (AM) method for solving double sparsity constrained minimization problem, where the decision variable vector is split into two blocks. The objective function is a separable smooth function in terms of the two blocks. We analyze the convergence of the method for the non-convex objective function and prove a rate of convergence of the norms of the partial gradient mappings. Then, we establish a non-asymptotic sub-linear rate of convergence under the assumption of convexity and the Lipschitz continuity of the gradient of the objective function. To solve the sub-problems of the AM method, we adopt the so-called iterative thresholding method and study their analytical properties. Finally, some future works are discussed.
关键词 ：
Alternating minimization Alternating minimization convergence rate convergence rate double sparsity constrained problem double sparsity constrained problem partial gradient mappings partial gradient mappings smooth function smooth function
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| GB/T 7714 | Gao, Huan , Li, Yingyi , Zhang, Haibin . The Analysis of Alternating Minimization Method for Double Sparsity Constrained Optimization Problem [J]. | ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH , 2020 , 37 (4) . |
| MLA | Gao, Huan et al. "The Analysis of Alternating Minimization Method for Double Sparsity Constrained Optimization Problem" . | ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 37 . 4 (2020) . |
| APA | Gao, Huan , Li, Yingyi , Zhang, Haibin . The Analysis of Alternating Minimization Method for Double Sparsity Constrained Optimization Problem . | ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH , 2020 , 37 (4) . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In this paper, we propose a hybrid Bregman alternating direction method of multipliers for solving the linearly constrained difference-of-convex problems whose objective can be written as the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function. At each iteration, we choose either subgradient step or proximal step to evaluate the concave part. Moreover, the extrapolation technique was utilized to compute the nonsmooth convex part. We prove that the sequence generated by the proposed method converges to a critical point of the considered problem under the assumption that the potential function is a Kurdyka-Lojasiewicz function. One notable advantage of the proposed method is that the convergence can be guaranteed without the Lischitz continuity of the gradient function of concave part. Preliminary numerical experiments show the efficiency of the proposed method.
关键词 ：
Alternating direction method of multipliers Alternating direction method of multipliers Bregman distance Bregman distance Kurdyka-Lojasiewicz function Kurdyka-Lojasiewicz function Linearly constrained difference-of-convex problems Linearly constrained difference-of-convex problems
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| GB/T 7714 | Tu, Kai , Zhang, Haibin , Gao, Huan et al. A hybrid Bregman alternating direction method of multipliers for the linearly constrained difference-of-convex problems [J]. | JOURNAL OF GLOBAL OPTIMIZATION , 2020 , 76 (4) : 665-693 . |
| MLA | Tu, Kai et al. "A hybrid Bregman alternating direction method of multipliers for the linearly constrained difference-of-convex problems" . | JOURNAL OF GLOBAL OPTIMIZATION 76 . 4 (2020) : 665-693 . |
| APA | Tu, Kai , Zhang, Haibin , Gao, Huan , Feng, Junkai . A hybrid Bregman alternating direction method of multipliers for the linearly constrained difference-of-convex problems . | JOURNAL OF GLOBAL OPTIMIZATION , 2020 , 76 (4) , 665-693 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Nonlinear conjugate gradient methods are among the most preferable and effortless methods to solve smooth optimization problems. Due to their clarity and low memory requirements, they are more desirable for solving large-scale smooth problems. Conjugate gradient methods make use of gradient and the previous direction information to determine the next search direction, and they require no numerical linear algebra. However, the utility of nonlinear conjugate gradient methods has not been widely employed in solving nonsmooth optimization problems. In this paper, a modified nonlinear conjugate gradient method, which achieves the global convergence property and numerical efficiency, is proposed to solve large-scale nonsmooth convex problems. The new method owns the search direction, which generates sufficient descent property and belongs to a trust region. Under some suitable conditions, the global convergence of the proposed algorithm is analyzed for nonsmooth convex problems. The numerical efficiency of the proposed algorithm is tested and compared with some existing methods on some large-scale nonsmooth academic test problems. The numerical results show that the new algorithm has a very good performance in solving large-scale nonsmooth problems.
关键词 ：
Conjugate gradient method Conjugate gradient method Global convergence Global convergence Moreau-Yosida regularization Moreau-Yosida regularization Nonsmooth large-scale problems Nonsmooth large-scale problems
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| GB/T 7714 | Woldu, Tsegay Giday , Zhang, Haibin , Zhang, Xin et al. A Modified Nonlinear Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization [J]. | JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS , 2020 , 185 (1) : 223-238 . |
| MLA | Woldu, Tsegay Giday et al. "A Modified Nonlinear Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization" . | JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 185 . 1 (2020) : 223-238 . |
| APA | Woldu, Tsegay Giday , Zhang, Haibin , Zhang, Xin , Fissuh, Yemane Hailu . A Modified Nonlinear Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization . | JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS , 2020 , 185 (1) , 223-238 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
矩阵特征值问题是机器学习、数据处理以及工程分析和计算中经常需要解决的问题之一.同伦算法是求解矩阵特征值的经典方法;自动微分可以有效、快速地计算出大规模问题相关函数的导数项,并且可以达到机器精度.充分利用自动微分的优点,设计自动微分技术与同伦算法相结合的方法求解矩阵特征值问题.数值实验验证了该算法的有效性.
关键词 ：
自动微分 自动微分 同伦算法 同伦算法 特征值 特征值
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| GB/T 7714 | 高欢 , 张海斌 , 涂凯 . 利用改进的同伦算法求解特征值问题 [J]. | 数学的实践与认识 , 2019 , 49 (01) : 223-229 . |
| MLA | 高欢 et al. "利用改进的同伦算法求解特征值问题" . | 数学的实践与认识 49 . 01 (2019) : 223-229 . |
| APA | 高欢 , 张海斌 , 涂凯 . 利用改进的同伦算法求解特征值问题 . | 数学的实践与认识 , 2019 , 49 (01) , 223-229 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
A positive-definite homogeneous multivariate form plays a critical role in the medical imaging and automatic control, and the definiteness of this form can be identified by a special structure tensor. In this paper, we first state the equivalence between the positive-definite multivariate form and the corresponding tensor and account for the links between the positive-definite tensor with a strong H-tensor. Then based on weak reducibility, some criteria were provided to identify strong H-tensors. Furthermore, with these relations, we establish an iterative scheme to identify the positive-definite multivariate homogeneous form and prove it is theoretically valid. Numerical experiments were given to illustrate the practicality of the scheme.
关键词 ：
homogeneous multivariate form homogeneous multivariate form iterative scheme iterative scheme Positive definiteness Positive definiteness strong H-tensor strong H-tensor weakly reducible weakly reducible
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| GB/T 7714 | Zhang, Kaili , Zhang, Haibin , Zhao, Pengfei et al. An iterative scheme for testing the positive definiteness of multivariate homogeneous forms* [J]. | INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS , 2019 , 96 (12) : 2461-2472 . |
| MLA | Zhang, Kaili et al. "An iterative scheme for testing the positive definiteness of multivariate homogeneous forms*" . | INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 96 . 12 (2019) : 2461-2472 . |
| APA | Zhang, Kaili , Zhang, Haibin , Zhao, Pengfei , Wang, Xueyong . An iterative scheme for testing the positive definiteness of multivariate homogeneous forms* . | INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS , 2019 , 96 (12) , 2461-2472 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Recently, some proximal-based alternating direction methods and alternating projection-based prediction-correction methods were proposed to solve the structured variational inequalities in Euclidean space . We note that the proximal-based alternating direction methods need to solve its subproblems exactly. However, the subproblems of the proximal-based alternating direction methods are too difficult to be solved exactly in many practical applications. We also note that the existing alternating projection based prediction-correction methods just can cope with the case that the underlying mappings are Lipschitz continuous. However, it could be difficult to verify their Lipschitz continuity condition, provided that the available information is only the mapping values. In this paper, we present a new alternating projection-based prediction-correction method for solving the structured variational inequalities, where the underlying mappings are continuous. In each iteration, we first employ a new Armijo linesearch to derive the predictors, and then update the next iterate via some minor computations. Under some mild assumptions, we establish the global convergence theorem of the proposed method. Preliminary numerical results are also reported to illustrate the effectiveness of the proposed method.
关键词 ：
alternating projection alternating projection Armijo linesearch Armijo linesearch continuous mappings continuous mappings global convergence global convergence prediction-correction method prediction-correction method Structured variational inequalities Structured variational inequalities
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| GB/T 7714 | Tu, K. , Zhang, H. B. , Xia, F. Q. . A new alternating projection-based prediction-correction method for structured variational inequalities [J]. | OPTIMIZATION METHODS & SOFTWARE , 2019 , 34 (4) : 707-730 . |
| MLA | Tu, K. et al. "A new alternating projection-based prediction-correction method for structured variational inequalities" . | OPTIMIZATION METHODS & SOFTWARE 34 . 4 (2019) : 707-730 . |
| APA | Tu, K. , Zhang, H. B. , Xia, F. Q. . A new alternating projection-based prediction-correction method for structured variational inequalities . | OPTIMIZATION METHODS & SOFTWARE , 2019 , 34 (4) , 707-730 . |
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