检索结果-南通市图书馆

NONMONOTONE LOCAL MINIMAX METHODS FOR FINDING MULTIPLE SADDLE POINTS

Journal of Computational Mathematics 2024年第3期42卷 851-884页

作者： Wei Liu Ziqing Xie Wenfan Yi South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou 510631China Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education) Hunan Normal UniversityChangshaHunan 410081China Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics School of MathematicsHunan UniversityChangshaHunan 410082China

In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to find multiple(unstable)saddle points of nonconvex functionals in Hilbert *** to traditional LMMs with monotone search strategies,this approach,which does not require strict decrease of the objective functional value at each iterative step,is observed to converge faster with less ***,based on a normalized iterative scheme coupled with a local peak selection that pulls the iterative point back onto the solution submanifold,by generalizing the Zhang-Hager(ZH)search strategy in the optimization theory to the LMM framework,a kind of normalized ZH-type nonmonotone step-size search strategy is introduced,and then a novel nonmonotone LMM is *** feasibility and global convergence results are rigorously carried out under the relaxation of the monotonicity for the functional at the iterative ***,in order to speed up the convergence of the nonmonotone LMM,a globally convergent Barzilai-Borwein-type LMM(GBBLMM)is presented by explicitly constructing the Barzilai-Borwein-type step-size as a trial step-size of the normalized ZH-type nonmonotone step-size search strategy in each ***,the GBBLMM algorithm is implemented to find multiple unstable solutions of two classes of semilinear elliptic boundary value problems with variational structures:one is the semilinear elliptic equations with the homogeneous Dirichlet boundary condition and another is the linear elliptic equations with semilinear Neumann boundary *** numerical results indicate that our approach is very effective and speeds up the LMMs significantly.

关键词： Multiple saddle points Local minimax method Barzilai-Borwein gradient method Normalized nonmonotone search strategy global convergence

来源：

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

A Weighted Flow related to a Trudinger–Moser Functional on Closed Riemann Surface

引用

Acta Mathematica Sinica,English Series 2024年第9期40卷 2244-2262页

作者： Peng Xiu YU School of Mathematics Renmin University of ChinaBeijing 100872P.R.China

In this paper,with(Σ,g)being a closed Riemann surface,we analyze the possible concentration behavior of a heat flow related to the Trudinger–Moser *** obtain a long time existence for the *** along some sequence of times t_(k)→+∞,we can deduce the convergence of the flow in H2(Σ).Furthermore,the limit function is a critical point of the Trudinger–Moser functional under certain constraint.

关键词： Trudinger-Moser inequality global convergence heat flow

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

SEMI-PROXIMAL POINT METHOD FOR NONSMOOTH CONVEX-CONCAVE MINIMAX OPTIMIZATION

引用

Journal of Computational Mathematics 2024年第3期42卷 617-637页

作者： Yuhong Dai Jiani Wang Liwei Zhang LSEC ICMSECAMSSChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences Dalian University of TechnologyDalian 116024China

Minimax optimization problems are an important class of optimization problems arising from modern machine learning and traditional research *** there have been many numerical algorithms for solving smooth convex-concave minimax problems,numerical algorithms for nonsmooth convex-concave minimax problems are *** paper aims to develop an efficient numerical algorithm for a structured nonsmooth convex-concave minimax problem.A semi-proximal point method(SPP)is proposed,in which a quadratic convex-concave function is adopted for approximating the smooth part of the objective function and semi-proximal terms are added in each *** construction enables the subproblems at each iteration are solvable and even easily solved when the semiproximal terms are cleverly *** prove the global convergence of our algorithm under mild assumptions,without requiring strong convexity-concavity *** the locally metrical subregularity of the solution mapping,we prove that our algorithm has the linear rate of *** numerical results are reported to verify the efficiency of our algorithm.

关键词： Minimax optimization Convexity-concavity global convergence Rate of con-vergence Locally metrical subregularity

来源：

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

ANonmonotone Projected Gradient Method for Multiobjective Problems on Convex Sets

引用

Journal of the Operations Research Society of China 2024年第2期12卷 410-427页

作者： Gabrie Anibal Carrizo Nadia Soledad Fazzio Maria Laura Schuverdt Department of Mathematics National University of the SouthBahia BlancaArgentina Department of Mathematics University of La PlataLa PlataArgentina

In this work we consider an extension of the classical scalar-valued projected gradient method for multiobjective problems on convex *** in Fazzio et al.(Optim Lett 13:1365-1379,2019)a parameter which controls the step length is considered and an updating rule based on the spectral gradient method from the scalar case is *** the present paper,we consider an extension of the traditional nonmonotone approach of Grippo et al.(SIAM J Numer Anal 23:707-716,1986)based on the maximum of some previous function values as suggested in Mita et al.(J Glob Optim 75:539-559,2019)for unconstrained multiobjective optimization *** prove the accumulation points of sequences generated by the proposed algorithm,if they exist,are stationary points of the original *** experiments are reported.

关键词： Multiobjective optimization Projected gradient methods Nonmonotone line search global convergence

来源：

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

global CONVERCENCE OF THE FLETCHER-REEVES ALGORITHM WITH INEXACT LINESEARCH

引用

Applied Mathematics(A Journal of Chinese Universities) 1995年第1期10卷 75-82页

作者： LIUGUANGHUI HANJIYE YINHONGXIA InstituteofAppliedMathematics AcademiaSinicaBeijing100080 InstituteofAppliedMathematics AcademisSinicaBeijing100080 DepartmentofMathematicsandAppliedPhysics BeijingUniversityofAeronauticsandAstronomicsBeijing100083

In this paper, we investigate the convergence properties of the FletcherReeves algorithm. Under conditions weaker than those in a Paper of M. Al-Baali,we get the global convergence of the Flincher-Reeves algorithm wit... 详细信息

关键词： 90C30 Fletcher-Reeves algorithm inexact linesearch global convergence

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

A CLASS OF TRUST REGION METHODS FOR LINEAR INEQUALITY CONSTRAINED OPTIMIZATION AND ITS THEORY ANALYSIS:*** AND global convergenceXIU NAIHUA

引用

Applied Mathematics(A Journal of Chinese Universities) 1995年第4期10卷 287-296页

作者： XIU NAIHUA Institute of Applied Mathematics Academia Sinica Beijing 100080 Current address: Department of Mathematics Hebei Teacher’s College Shijiazhuang 050091).

A class of trust region methods for solving linear inequality constrained problems is proposed in this paper. It is shown that the algorithm is of global *** algorithm uses a version of the two-sided projection and the strategy of the unconstrained trust region methods. It keeps the good convergence properties of the unconstrained case and has the merits of the projection method. In some sense, our algorithm can be regarded as an extension and improvement of the projected type algorithm.

关键词： Linear inequality constrained optimization trust region method global convergence

来源：

维普期刊数据库

同方期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

global COVERGENCE OF THE NON-QUASI-NEWTON METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS

引用

Applied Mathematics(A Journal of Chinese Universities) 2006年第3期21卷 276-288页

作者： Liu Hongwei Wang Mingjie Li Jinshan Zhang Xiangsun School of Economics Renmin University of China Beijing 100872 China Department of Mathematics Capital NormaIUniversity Beijing 100037 China Institute of Applied Mathematics Academy of Mathematics ＆ Systems Science Chinese Academy of Sciences Beijing 100080 China

In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.

关键词： non-quasi-Newton method inexact line search global convergence unconstrained optimization,superlinear convergence.

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

一种修正的HS共轭梯度法及全局收敛性

引用

高等学校计算数学学报 2010年第2期32卷 150-156页

作者：王开荣刘金魁邹黎敏重庆大学数学与统计学院重庆三峡学院数学与计算机科学学院

1引言考虑无约束极小化问题:（?）,（1）其中f（x）连续可微,其梯度函数用g（x）表示.共轭梯度法求解（1）的常用迭代格式为:x;=x;+α;d;,（2）(?)（3）其中g;=▽f（x;）,α;≥0是由某种线搜索得到的步长因子;d;为搜索方向,β;为标量,β... 详细信息

1引言考虑无约束极小化问题:（?）,（1）其中f（x）连续可微,其梯度函数用g（x）表示.共轭梯度法求解（1）的常用迭代格式为:x;=x;+α;d;,（2）(?)（3）其中g;=▽f（x;）,α;≥0是由某种线搜索得到的步长因子;d;为搜索方向,β;为标量,β;的不同选择产生了不同的共轭梯度法.著名的β;公式有:

关键词： unconstrained optimization conjugate gradient method Hestenes-Stiefel method Wolfe line search global convergence

来源：

同方期刊数据库评论

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

由FR共轭梯度法控制的两类优化算法的全局收敛性

引用

高等学校计算数学学报 2000年第4期22卷 311-318页

作者：杜学武徐成贤西安交通大学科学计算与应用软件系!西安710049 焦作工学院基础科学部!焦作454159

In this paper, we prove that two classes of general methods for unconstrained optimization which is constrained by the Fletcher-Reeves conjugate gradient method are globally convergent under a kind of inexact line sea... 详细信息

关键词： unconstrained optimization conjugate gradient method Fletcher-Reeves method global convergence line search.

来源：

同方期刊数据库评论

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

一种充分下降的PRP共轭梯度法的全局收敛性

引用

高等学校计算数学学报 2013年第2期35卷 148-158页

作者：李敏屈爱平怀化学院数学与应用数学系

Yu and Guan proposed a sufficient descent PRP conjugate gradient method(DPRP method) and established the global convergence based on some *** no convergence results were obtained for nonconvex objective functions with standard Armijo line search or Wolfe line *** this paper,a cautious DPRP method is *** is showed that the proposed method is globally convergent if the Armijo line search or the Wolfe line search is *** numerical results show that the proposed method is efficient.

关键词： sufficient descent PRP method Armijo line search Wolfe line search global convergence

来源：

同方期刊数据库评论

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

欢迎您,

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

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

请选择保存的检索档案：

请选择收藏分类：

通借通还

欢迎您,

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

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

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：