检索结果-南通市图书馆

An Improved Feasible QP-free Algorithm for Inequality Constrained Optimization

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2012年第12期28卷 2475-2488页

作者： Zhi Bin ZHU jin bao jian College of Mathematics and Computing Science Guilin University of Electronic Technology College of Mathematics and Informational Science Guangxi University College of Mathematics and Informational Science Yulin Normal University

In this paper, an improved feasible QP-free method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction. In view of the computational cost, the most attractive feature of the new algorithm is that only one system of linear equations is required to obtain the revised feasible descent direction. Thereby, per single iteration, it is only necessary to solve three systems of linear equations with the same coefficient matrix. In particular, without the positive definiteness assumption on the Hessian estimate, the proposed algorithm is still global convergence. Under some suitable conditions, the superlinear convergence rate is obtained.

关键词： Inequality constrained optimization feasible QP-free method system of linear equations,global convergence superlinear convergence rate

A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2007年第3期23卷 395-410页

作者： jin-bao jian Ran Quan Qing-jie Hu College of Mathematics and Information Science Guangxi University Nanning 530004 China College of Electrical Engineering Guangxi University Nanning 530004 Chin Department of Information Hunan Business College Changsha 410205 China

In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming （SQP）, a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming （QP） which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported.

关键词： Minimax problems SQP algorithm global convergence superlinear convergence

A Feasible Point Method with Bundle Modification for Nonsmooth Convex Constrained Optimization

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2018年第2期34卷 254-273页

作者： jin-bao jian Chun-ming TANG Lu SHI College of Mathematics and Information Science Guangxi University Nanning 530004 China College of Science Guangxi University of Nationalities Nanning 530007 China Xingjian College of Science and Liberal Arts Guangxi University Nanning 530005 China

In this paper, a bundle modification strategy is proposed for nonsmooth convex constrained min- imization problems. As a result, a new feasible point bundle method is presented by applying this strategy. Whenever the stability center is updated, some points in the bundle will be substituted by new ones which have lower objective values and/or constraint values, aiming at getting a better bundle. The method generates feasible serious iterates on which the objective function is monotonically decreasing. Global convergence of the algorithm is established, and some preliminary numerical results show that our method performs better than the standard feasible point bundle method.

关键词： nonsmooth optimization feasible point method bundle modification global convergence

A Bregman-style Partially Symmetric Alternating Direction Method of Multipliers for Nonconvex Multi-block Optimization

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2023年第2期39卷 354-380页

作者： Peng-jie LIU jin-bao jian Guo-dong MA School of Mathematics China University of Mining and TechnologyXuzhou 221116China College of Mathematics and Physics Center for Applied Mathematics of GuangxiGuangxi Minzu UniversityNanning 530006China

The alternating direction method of multipliers(ADMM)is one of the most successful and powerful methods for separable minimization *** on the idea of symmetric ADMM in two-block optimization,we add an updating formula for the Lagrange multiplier without restricting its position for multiblock ***,combining with the Bregman distance,in this work,a Bregman-style partially symmetric ADMM is presented for nonconvex multi-block optimization with linear constraints,and the Lagrange multiplier is updated twice with different relaxation factors in the iteration *** the suitable conditions,the global convergence,strong convergence and convergence rate of the presented method are analyzed and ***,some preliminary numerical results are reported to support the correctness of the theoretical assertions,and these show that the presented method is numerically effective.

关键词： nonconvex optimization multi-block optimization alternating direction method with multipliers Kurdyka-Lojasiewicz property convergence rate

A New QP-free Algorithm Without a Penalty Function or a Filter for Nonlinear Semidefinite Programming

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2020年第3期36卷 714-736页

作者： jian-ling LI Zhen-ping YANG Jia-qi WU jin-bao jian College of Mathematics and Information Science Guangxi UniversityNanning 530004China School of Mathematics Jiaying UniversityMeizhou 514015China College of Science Guangxi University for NationalitiesNanning 530006China

In this paper,we present a QP-free algorithm without a penalty function or a filter for nonlinear semidefinite *** each iteration,two systems of linear equations with the same coefficient matrix are solved to determine search direction;the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently *** is no feasibility restoration phase in our algorithm,which is necessary for traditional filter *** proposed algorithm is globally convergent under some mild *** numerical results indicate that the proposed algorithm is comparable.

关键词： nonlinear semidefinite programming QP-free penalty-free nonmonotone line search global convergence

A New Sequential Systems of Linear Equations Algorithm of Feasible Descent for Inequality Constrained Optimization

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2010年第12期26卷 2399-2420页

作者： jin bao jian Dao Lan HAN Qing Juan XU College of Mathematics and Infornation Science Guangxi University Nanning 530004 P. R. China College of Mathematics and Computer Science Guangxi University for NationalitiesNanning 530006 P. R. China College of Electrical Engineering Guangxi University Nanning 530004 P. R. China Department of Mathematics Shanghai University Shanghai 200444 P. R. China College of Mathematical Science Guangxi Teachers Education University Nanning 530001 P. R. China

Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.

关键词： Inequality constraints nonlinear optimization systems of linear equations global conver-gence superlinear convergence

Convergence of Bregman Peaceman–Rachford Splitting Method for Nonconvex Nonseparable Optimization

在线全文

学校读者我要写书评

暂无评论

Journal of the Operations Research Society of China 2023年第4期11卷 707-733页

作者： Peng-Jie Liu jin-bao jian Bo He Xian-Zhen jiang College of Mathematics and Physics Guangxi Key Laboratory of Hybrid Computation and IC Design AnalysisCenter for Applied Mathematics and Artificial IntelligenceGuangxi University for NationalitiesNanning530006GuangxiChina College of Mathematics and Information Science Guangxi UniversityNanning530004GuangxiChina School of Mathematics China University of Mining and TechnologyXuzhou221116JiangsuChina

This work is about a splitting method for solving a nonconvex nonseparable optimization problem with linear constraints,where the objective function consists of two separable functions and a coupled ***,based on the ideas from Bregman distance and Peaceman–Rachford splitting method,the Bregman Peaceman–Rachford splitting method with different relaxation factors for the multiplier is ***,the global and strong convergence of the proposed algorithm are proved under general conditions including the region of the two relaxation factors as well as the crucial Kurdyka–Łojasiewicz ***,when the associated Kurdyka–Łojasiewicz property function has a special structure,the sublinear and linear convergence rates of the proposed algorithm are ***,some preliminary numerical results are shown to indicate the effectiveness of the proposed algorithm.

关键词： Nonconvex nonseparable optimization Peaceman-Rachford splitting method Bregman distance Kurdyka-Łojasiewicz inequality Convergence rate

A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting:Convergence and Rate Analyses

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of the Operations Research Society of China 2024年第2期12卷 298-340页

作者： Peng-Jie Liu jin-bao jian Hu Shao Xiao-Quan Wang Jia-Wei Xu Xiao-Yu Wu School of Mathematics Jiangsu Center for Applied MathematicsChina University of Mining and TechnologyXuzhou 221116JiangsuChina School of Mathematics and Physics Center for Applied Mathematics of GuangxiGuangxi Minzu UniversityNanning 530006GuangxiChina Department of Civil and Environmental Engineering The Hong Kong Polytechnic UniversityHong KongChina School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105HunanChina

This work explores a family of two-block nonconvex optimization problems subject to linear *** first introduce a simple but universal Bregman-style improved alternating direction method of multipliers(ADMM)based on the iteration framework of ADMM and the Bregman ***,we utilize the smooth performance of one of the components to develop a linearized version of *** to the traditional ADMM,both proposed methods integrate a convex combination strategy into the multiplier update *** each proposed method,we demonstrate the convergence of the entire iteration sequence to a unique critical point of the augmented Lagrangian function utilizing the powerful Kurdyka–Łojasiewicz property,and we also derive convergence rates for both the sequence of merit function values and the iteration ***,some numerical results show that the proposed methods are effective and encouraging for the Lasso model.

关键词： Nonconvex optimization Alternating direction method of multipliers Kurdyka-Lojasiewicz property Convergence rate

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

具有充分下降性的两个共轭梯度法

数学学报（中文版） 2014年第2期57卷 365-372页

作者：江羡珍简金宝马国栋玉林师范学院数学与信息科学学院玉林537000 广西大学数学与信息科学学院南宁530004

对无约束优化问题,本文给出了两个改进的共轭梯度法公式.在不依赖于任何线搜索条件下,由新公式所产生的算法方向均是充分下降的,且在标准Wolfe非精确线搜索条件下,算法都具有全局收敛性.最后,对新算法进行大量的比对试验,数值结果表明... 详细信息

对无约束优化问题,本文给出了两个改进的共轭梯度法公式.在不依赖于任何线搜索条件下,由新公式所产生的算法方向均是充分下降的,且在标准Wolfe非精确线搜索条件下,算法都具有全局收敛性.最后,对新算法进行大量的比对试验,数值结果表明所提方法是有效的.

关键词：无约束优化共轭梯度法充分下降性全局收敛性