检索结果-内蒙古大学图书馆

Superiorization methodology and perturbation resilience of inertial proximal gradient algorithm with application to signal recovery

引用

JOURNAL OF SUPERCOMPUTING 2020年第12期76卷 9456-9477页

作者： Pakkaranang, Nuttapol Kumam, Poom Berinde, Vasile Suleiman, Yusuf I. KMUTT Ctr Excellence Theoret & Computat Sci TaCS CoE KMUTT Fixed Point Theory & Applicat Res Grp KMUTT Sci Lab Bldg126 Pracha Uthit Rd Bangkok 10140 Thailand KMUTT KMUTTFixed Point Res Lab Dept Math Fac Sci Room SCL 802 Fixed Point LabSci Lab Bldg Bangkok 10140 Thailand China Med Univ China Med Univ Hosp Dept Med Res Taichung 40402 Taiwan Tech Univ Cluj Napoca Dept Math & Comp Sci North Univ Ctr Baia Mare Victorie 76 Baia Mare 430072 Romania Kano Univ Sci & Technol Dept Math PMB 3042 Kano Nigeria

In this paper, we construct a novel algorithm for solving non-smooth composite optimization problems. By using inertial technique, we propose a modified proximal gradient algorithm with outer perturbations, and under standard mild conditions, we obtain strong convergence results for finding a solution of composite optimization problem. Based on bounded perturbation resilience, we present our proposed algorithm with the superiorization method and apply it to image recovery problem. Finally, we provide the numerical experiments to show efficiency of the proposed algorithm and comparison with previously known algorithms in signal recovery.

关键词： Composite optimization problems proximal gradient algorithm Inertial algorithm Superiorization methodology Bounded perturbation resilience

来源：评论

学校读者我要写书评

暂无评论

On the convergence of the iterates of proximal gradient algorithm with extrapolation for convex nonsmooth minimization problems

引用

JOURNAL OF GLOBAL OPTIMIZATION 2019年第3期75卷 767-787页

作者： Wen, Bo Xue, Xiaoping Hebei Univ Technol Inst Math Tianjin Peoples R China Harbin Inst Technol Dept Math Harbin Heilongjiang Peoples R China Harbin Inst Technol Inst Adv Study Math Harbin Heilongjiang Peoples R China

In this paper, we consider the proximal gradient algorithm with extrapolation for solving a class of convex nonsmooth minimization problems. We show that for a large class of extrapolation parameters including the extrapolation parameters chosen in FISTA (Beck and Teboulle in SIAM J Imaging Sci 2:183-202, 2009), the successive changes of iterates go to 0. Moreover, based on the Lojasiewicz inequality, we establish the global convergence of iterates generated by the proximal gradient algorithm with extrapolation with an additional assumption on the extrapolation coefficients. The assumption is general enough to allow the threshold of the extrapolation coefficients to be 1. In particular, we prove the length of the iterates is finite. Finally, we perform numerical experiments on the least squares problems with l(1) regularization to illustrate our theoretical results.

关键词： Convex minimization proximal gradient algorithm Extrapolation Lojasiewicz inequality Convergence

来源：评论

学校读者我要写书评

暂无评论

A DISTRIBUTED FLEXIBLE DELAY-TOLERANT proximal gradient algorithm

引用

SIAM JOURNAL ON OPTIMIZATION 2020年第1期30卷 933-959页

作者： Mishchenko, Konstantin Iutzeler, Franck Malick, Jerome KAUST Thuwal Saudi Arabia Univ Grenoble Alpes Lab Jean Kuntzmann Grenoble France CNRS Lab Jean Kuntzmann Grenoble France

We develop and analyze an asynchronous algorithm for distributed convex optimization when the objective can be written as a sum of smooth functions, local to each worker, and a nonsmooth function. Unlike many existing methods, our distributed algorithm is adjustable to various levels of communication cost, delays, machines' computational power, and functions' smoothness. A unique feature is that the step sizes do not depend on communication delays nor number of machines, which is highly desirable for scalability. We prove that the algorithm converges linearly in the strongly convex case, and provide guarantees of convergence for the non-strongly convex case. The obtained rates are the same as the vanilla proximal gradient algorithm over some introduced epoch sequence that subsumes the delays of the system. We provide numerical results on large-scale machine learning problems to demonstrate the merits of the proposed method.

关键词： distributed optimization proximal gradient algorithm convex optimization asynchronous methods

来源：评论

学校读者我要写书评

暂无评论

On the proximal gradient algorithm with Alternated Inertia

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2018年第3期176卷 688-710页

作者： Iutzeler, Franck Malick, Jerome Univ Grenoble Alpes Grenoble France CNRS LJK Grenoble France

In this paper, we investigate attractive properties of the proximal gradient algorithm with inertia. Notably, we show that using alternated inertia yields monotonically decreasing functional values, which contrasts with usual accelerated proximal gradient methods. We also provide convergence rates for the algorithm with alternated inertia, based on local geometric properties of the objective function. The results are put into perspective by discussions on several extensions (strongly convex case, non-convex case, and alternated extrapolation) and illustrations on common regularized optimization problems.

关键词： proximal gradient algorithm Accelerated methods Kurdyka-Lojasiewicz inequality

来源：评论

学校读者我要写书评

暂无评论

Control proximal gradient algorithm for image l1 regularization

引用

SIGNAL IMAGE AND VIDEO PROCESSING 2019年第6期13卷 1113-1121页

作者： El Mouatasim, Abdelkrim Univ Ibn Zohr Fac Polydisplinaire BP 284 Ouarzazate 45800 Morocco

We consider a control proximal gradient algorithm (CPGA) for solving the minimization of a nonsmooth convex function. In particular, the convex function is an l(1) regularized least squares function derived by the discretized l(1) norm models arising in image processing. This proximal gradient algorithm with the control step size is attractive due to its simplicity. However, this method is also known to converge quite slowly. In this paper, we present a fast control proximal gradient algorithm by adding Nesterov step. It preserves the computational simplicity of proximal gradient methods with a convergence rate 1/k(2). It is proven to be better than the existing methods both theoretically and practically. The initial numerical results for performing the image deblurring demonstrate the efficiency of CPGA when it is compared to the existing fast iterative shrinkage-thresholding algorithms.

关键词： proximal gradient algorithm Nesterov algorithm Step-size control l(1) Regularization Image deblurring FISTA

来源：评论

学校读者我要写书评

暂无评论

A diagonal finite element-projection-proximal gradient algorithm for elliptic optimal control problem

引用

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2023年 148卷 256-268页

作者： Lin, Jitong Chen, Xuesong Guangdong Univ Technol Sch Math & Stat Guangzhou 510520 Peoples R China

A diagonal finite element-projection-proximal gradient (DFE-P-PG) algorithm and its accelerated forms for elliptic optimal control problem with ��1-control cost are proposed in this paper. Firstly, the elliptic optimal control problem is discretized by the diagonal finite element method (DFEM). Then the discrete problem is optimized by projection-proximal gradient (P-PG) algorithm. The global convergence of DFE-P-PG algorithm is proven. In addition, two accelerated methods are used to enhance the convergence rate of DFE-P-PG algorithm. Numerical examples are performed to illustrate the efficiency and effectiveness of DFE-P-PG algorithm.

关键词： Optimal control problem Finite element method proximal gradient algorithm Accelerated method Convergence analysis

来源：评论

学校读者我要写书评

暂无评论

An inexact proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth optimization problems

引用

JOURNAL OF INEQUALITIES AND APPLICATIONS 2019年第1期2019卷 1-16页

作者： Jia, Zehui Wu, Zhongming Dong, Xiaomei Nanjing Univ Informat Sci & Technol Sch Math & Stat Dept Informat & Comp Sci Nanjing Jiangsu Peoples R China Southeast Univ Sch Econ & Management Nanjing Jiangsu Peoples R China Nanjing Normal Univ Sch Math Sci Nanjing Jiangsu Peoples R China

In this paper, we propose an inexact version of proximal gradient algorithm with extrapolation for solving a class of nonconvex nonsmooth optimization problems. Specifically, the subproblem in proximal gradient algorithm with extrapolation is allowed to be solved inexactly by certain relative error criterion, in the sense that the criterion can be updated adaptively in each iteration. Under the assumption that an auxiliary function satisfies the Kurdyka-ojasiewicz (KL) inequality, we prove that the iterative sequence generated by the inexact proximal gradient algorithm with extrapolation converges to a stationary point of the considered problem. Furthermore, the convergence rate of the proposed algorithm can be established when the KL exponent is known. Moreover, we illustrate the advantage by applying the algorithm to solve a nonconvex optimization problem.

关键词： Nonconvex minimization proximal gradient algorithm Relative error criterion Extrapolation Global convergence

来源：评论

学校读者我要写书评

暂无评论

Bregman proximal gradient algorithm With Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems

引用

IEEE ACCESS 2019年 7卷 126515-126529页

作者： Zhang, Xiaoya Barrio, Roberto Angeles Martinez, M. Jiang, Hao Cheng, Lizhi Natl Univ Def Technol Dept Math Changsha 410073 Hunan Peoples R China Univ Zaragoza Dept Matemat Aplicada E-50009 Zaragoza Spain Natl Univ Def Technol Coll Comp Changsha 410073 Hunan Peoples R China

In this paper, we consider an accelerated method for solving nonconvex and nonsmooth minimization problems. We propose a Bregman proximal gradient algorithm with extrapolation (BPGe). This algorithm extends and accelerates the Bregman proximal gradient algorithm (BPG), which circumvents the restrictive global Lipschitz gradient continuity assumption needed in proximal gradient algorithms (PG). The BPGe algorithm has a greater generality than the recently introduced proximal gradient algorithm with extrapolation (PGe) and, in addition, due to the extrapolation step, BPGe converges faster than the BPG algorithm. Analyzing the convergence, we prove that any limit point of the sequence generated by BPGe is a stationary point of the problem by choosing the parameters properly. Besides, assuming Kurdyka-Lojasiewicz property, we prove that all the sequences generated by BPGe converge to a stationary point. Finally, to illustrate the potential of the new method BPGe, we apply it to two important practical problems that arise in many fundamental applications (and that not satisfy global Lipschitz gradient continuity assumption): Poisson linear inverse problems and quadratic inverse problems. In the tests the accelerated BPGe algorithm shows faster convergence results, giving an interesting new algorithm.

关键词： Bregman proximal gradient algorithm with extrapolation bregman distance proximal gradient algorithm smooth adaptive condition relative weakly convexity

来源：评论

学校读者我要写书评

暂无评论

Strong convergence of over-relaxed multi-parameter proximal scaled gradient algorithm and superiorization

引用

OPTIMIZATION 2021年第3期70卷 461-480页

作者： Guo, Yanni Zhao, Xiaozhi Civil Aviat Univ China Coll Sci Tianjin Peoples R China

In this paper, we propose an over-relaxed proximal scaled gradient algorithm for solving the non-smooth composite optimization problem in Hilbert space. We prove the strong convergence and the bounded perturbation resilience of this algorithm under some mild conditions. We also list the superiorized version of the algorithm. We apply the algorithms to the problem to illustrate the performance and validity. The numerical examples show that the over-relaxed algorithm can achieve fewer iteration steps and less running times in comparison to the under-relaxed algorithm, and that the superiorization algorithm has the minimum iterative steps among the three algorithms.

关键词： Strong convergence bounded perturbation resilience proximal gradient algorithm over-relaxed convex minimization problem

来源：评论

学校读者我要写书评

暂无评论

A Mini-Batch proximal Stochastic Recursive gradient algorithm with Diagonal Barzilai–Borwein Stepsize

引用

Journal of the Operations Research Society of China 2023年第2期11卷 277-307页

作者： Teng-Teng Yu Xin-Wei Liu Yu-Hong Dai Jie Sun School of Artificial Intelligence Hebei University of TechnologyTianjin 300401China Institute of Mathematics Hebei University of TechnologyTianjin 300401China LSEC ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Business National University of SingaporeSingapore 119245Singapore

Many machine learning problems can be formulated as minimizing the sum of a function and a non-smooth regularization *** stochastic gradient methods are popular for solving such composite optimization *** propose a minibatch proximal stochastic recursive gradient algorithm SRG-DBB,which incorporates the diagonal Barzilai–Borwein(DBB)stepsize strategy to capture the local geometry of the *** linear convergence and complexity of SRG-DBB are analyzed for strongly convex *** further establish the linear convergence of SRGDBB under the non-strong convexity ***,it is proved that SRG-DBB converges sublinearly in the convex *** experiments on standard data sets indicate that the performance of SRG-DBB is better than or comparable to the proximal stochastic recursive gradient algorithm with best-tuned scalar stepsizes or BB ***,SRG-DBB is superior to some advanced mini-batch proximal stochastic gradient methods.

关键词： Stochastic recursive gradient proximal gradient algorithm Barzilai-Borwein method Composite optimization

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：