检索结果-内蒙古大学图书馆

Finite Convergence of the proximal point algorithm for Variational Inequality Problems

SET-VALUED AND VARIATIONAL ANALYSIS 2013年第2期21卷 297-309页

作者： Matsushita, Shin-ya Xu, Li Akita Prefectural Univ Dept Elect & Informat Syst Akita Japan

In this paper, we establish sufficient conditions for guaranteeing finite termination of an arbitrary algorithm for solving a variational inequality problem in a Banach space. Applying these conditions, it shows that ... 详细信息

关键词： Variational inequality problem Weak sharp minima Finite termination proximal point algorithm Banach space Metric projection Generalized projection

来源：评论

学校读者我要写书评

暂无评论

A GENERALIZATION OF THE proximal point algorithm

引用

SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1990年第3期28卷 503-512页

作者： HA, CD VIRGINIA COMMONWEALTH UNIV DEPT MATH SCIRICHMONDVA 23284

The problem considered in this paper is to find a solution to the generalized equation $0 \in T(x,y)$, where T is a maximal monotone operator on the product $H_1 \times H_2 $ of two Hilbert spaces $H_1 $ and $H_2 $. We give a generalization of the proximal map and the proximal point algorithm in which the proposed iterative procedure is based on just one variable. Applying to convex programming problems, instead of adding a quadratic term for all variables as in the proximal point algorithm, a quadratic term for a subset of variables is added. This paper proves that under a mild assumption our algorithm has the same convergence properties as the regular proximal point algorithm.

关键词： 47H05 49D45 90C25 monotone operator convex programming proximal point algorithm generalized equation

来源：评论

学校读者我要写书评

暂无评论

A Self-adaptive proximal point algorithm for Signal Reconstruction in Compressive Sensing

A Self-adaptive Proximal Point Algorithm for Signal Reconstr...

引用

IEEE International Conference on Signal and Image Processing (ICSIP)

作者： Huai, Kaizhan Li, Yejun Ni, Mingfang Yu, Zhanke Wang, Xiaoguo PLA Univ Sci & Technol Inst Commun Engn Nanjing Jiangsu Peoples R China Xian Commun Inst Xian Shaanxi Peoples R China

ISBN: (纸本)9781509023776

Compressive sensing (CS) is a new framework for simulations sensing and compressive. How to reconstruct a sparse signal from limited measurements is the key problem in CS. For solving the reconstruction problem of a sparse signal, we proposed a self-adaptive proximal point algorithm (PPA). This algorithm can handle the sparse signal reconstruction by solving a substituted problem-l(1) problem. At last, the numerical results shows that the proposed method is more effective compared with the compressive sampling matching pursuit (CoSaMP).

关键词： compressive sensing signal reconstruction proximal point algorithm self-adaptive

来源：评论

学校读者我要写书评

暂无评论

Primal-dual proximal point algorithm for linearly constrained convex programming problems

引用

Computational Optimization and Applications 1992年第2期1卷 207-226页

作者： Ibaraki, Satoru Fukushima, Masao Ibaraki, Toshihide Department of Applied Mathematical and Physics Faculty of Engineering Kyoto University Kyoto 606 Japan

A primal-dual version of the proximal point algorithm is developed for linearly constrained convex programming problems. The algorithm is an iterative method to find a saddle point of the Lagrangian of the problem. At each iteration of the algorithm, we compute an approximate saddle point of the Lagrangian function augmented by quadratic proximal terms of both primal and dual variables. Specifically, we first minimize the function with respect to the primal variables and then approximately maximize the resulting function of the dual variables. The merit of this approach exists in the fact that the latter function is differentiable and the maximization of this function is subject to no constraints. We discuss convergence properties of the algorithm and report some numerical results for network flow problems with separable quadratic costs. © 1992 Kluwer Academic Publishers.

关键词： convex programming Lagrangian primal-dual method proximal point algorithm

来源：评论

学校读者我要写书评

暂无评论

Modified proximal point algorithm for extended linear-quadratic programming

引用

Computational Optimization and Applications 1992年第2期1卷 185-205页

作者： Zhu, Ciyou Department of Mathematical Sciences Johns Hopkins University Baltimore 21218 MD United States

Extended linear-quadratic programming arises as a flexible modeling scheme in dynamic and stochastic optimization, which allows for penalty terms and facilitates the use of duality. Computationally it raises new challenges as well as new possibilities in large-scale applications. Recent efforts have been focused on the fully quadratic case ([15] and [23]), while relying on the fundamental proximal point algorithm (PPA) as a shell of "outer" iterations when the problem is not fully quadratic. In this paper, we focus on the nonfully quadratic cases by proposing some new variants of the fundamental PPA. We first construct a continuously differentiable saddle function S(u, v) through infimal convolution in such a way that the optimal primal-dual pairs of the original problem are just the saddle points of S(u, v) on the whole space. Then the original extended linear-quadratic-programming problem reduces to solving the nonlinear equation ∇S(u, v)=0. We then embed the fundamental PPA and some of its previous variants in the framework of a Newton-like iteration for this equation. After revealing the local quadratic structure of S near the solution, we derive new extensions of the fundamental PPA. In numerical tests, the modified iteration scheme based on the quasi-Newton update formula outperforms the fundamental PPA considerably. © 1992 Kluwer Academic Publishers.

关键词： extended linear-quadratic programming large-scale numerical optimization proximal point algorithm quasi-Newton methods

来源：评论

学校读者我要写书评

暂无评论

EFFECTIVE STRONG CONVERGENCE OF THE proximal point algorithm IN CAT(0) SPACES

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS

引用

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS 2018年第2期2卷 219-228页

作者： Leustean, Laurentiu Sipos, Andrei Univ Bucharest Res Inst Univ Bucharest ICUB Bd M Kogalniceanu 36-46 Bucharest 050107 Romania Univ Bucharest Fac Math & Comp Sci Acad 14 Bucharest 010014 Romania Tech Univ Darmstadt Dept Math Schlossgartenstr 7 D-64289 Darmstadt Germany Romanian Acad Simion Stoilow Inst Math Calea Grivitei 21 Bucharest 010702 Romania

We apply methods of proof mining to obtain uniform quantitative bounds on the strong convergence of the proximal point algorithm for finding minimizers of convex, lower semicontinuous, proper functions in CAT(0) spaces. Thus, for uniformly convex functions, we compute rates of convergence, while, for totally bounded CAT(0) spaces, we apply methods introduced by Kohlenbach, Leustean and Nicolae to compute rates of metastability.

关键词： proximal point algorithm CAT(0) spaces Proof mining Rates of convergence Rates of metastability

来源：评论

学校读者我要写书评

暂无评论

WEAK AND LINEAR CONVERGENCE OF A GENERALIZED proximal point algorithm WITH ALTERNATING INERTIAL STEPS FOR A MONOTONE INCLUSION PROBLEM

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS

引用

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS 2021年第6期5卷 881-892页

作者： Shehu, Yekini Ezeora, Jeremiah N. Zhejiang Normal Univ Dept Math Jinhua Zhejiang Peoples R China Univ Port Harcourt Dept Math & Stat Port Harcourt Rivers State Nigeria

The proximal point algorithm (PPA) is a powerful tool for solving monotone inclusion problems. Recently, Tao and Yuan [On the optimal linear convergence rate of a generalized proximal point algorithm, J. Sci. Comput. 74 (2018), 826-850] proposed a generalized PPA (GPPA) for finding a zero point of a maximal monotone operator, and obtained the linear convergence rate of the generalized PPA. In this paper, we consider accelerating the GPPA with the aid of the inertial extrapolation. We propose a generalized proximal point algorithm with alternating inertial steps solving monotone inclusion problem, and obtain weak convergence results under some mild conditions. When the inverse of the involved monotone operator is Lipschitz continuous at the origin, we prove that the iterative sequence generated by our generalized proximal point algorithm is linearly convergent. The Fejer monotonicity of even subsequences of the iterative sequence is also recovered. Finally, we give some priori and posteriori error estimates of our generated sequences.

关键词： Alternated inertial step Maximal monotone operator proximal point algorithm Weak and linear convergence

来源：评论

学校读者我要写书评

暂无评论

A proximal point algorithm for finding minimizers and fixed points of quasi-pseudo-contractive mappings in CAT(0) spaces

引用

JOURNAL OF FIXED point THEORY AND APPLICATIONS 2021年第1期23卷 5-5页

作者： Chang, Shih-sen Wang, L. Zhao, L. C. Liu, X. D. China Med Univ Ctr Gen Educ Taichung 40402 Taiwan Yunnan Univ Finance & Econ Kunming 650221 Yunnan Peoples R China Yibin Univ Dept Math Yibin 644007 Sichuan Peoples R China

The purpose of this article is twofold. One is to establish a proximal point algorithm for finding a minimizer of a proper convex and lower semi-continuous function and fixed points of quasi-pseudo-contractive mappings in CAT(0) spaces. The other is to point out and correct a basic and conceptual error in a paper of Ugwunnadi et al. [Theorem 3.1, J. Fixed point Theory Appl. (2018) 20: 82].

关键词： proximal point algorithm demi-contractive mapping quasi-pseudo-contractive mapping quasi-nonexpansive mappings CAT(0) space

来源：评论

学校读者我要写书评

暂无评论

A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces

引用

JOURNAL OF INEQUALITIES AND APPLICATIONS 2018年第1期2018卷 235-235页

作者： Chang, Shih-sen Yao, Jen-Chih Wen, Ching-Feng Wang, Lin China Med Univ Ctr Gen Educ Taichung Taiwan Kaohsiung Med Univ Ctr Fundamental Sci Kaohsiung Taiwan Kaohsiung Med Univ Res Ctr Nonlinear Anal & Optimizat Kaohsiung Taiwan Kaohsiung Med Univ Hosp Dept Med Res Kaohsiung Taiwan Yunnan Univ Finance & Econ Coll Stat & Math Kunming Yunnan Peoples R China

The purpose of this article is to propose a modified viscosity implicit-type proximal point algorithm for approximating a common solution of a monotone inclusion problem and a fixed point problem for an asymptotically nonexpansive mapping in Hadamard spaces. Under suitable conditions, some strong convergence theorems of the proposed algorithms to such a common solution are proved. Our results extend and complement some recent results in this direction.

关键词： Hadamard space CAT(0) space Viscosity implicit approximation methods Monotone mapping proximal point algorithm

来源：评论

学校读者我要写书评

暂无评论

The modified proximal point algorithm in Hadamard spaces

引用

JOURNAL OF INEQUALITIES AND APPLICATIONS 2018年第1期2018卷 124-124页

作者： Chang, Shih-sen Wang, Lin Wen, Ching-Feng Zhang, Jian Qiang China Med Univ Ctr Gen Educ Taichung Taiwan Yunnan Univ Finance & Econ Coll Stat & Math Kunming Yunnan Peoples R China Kaohsiung Med Univ Ctr Fundamental Sci Kaohsiung Taiwan

The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces.

关键词： Hadamard space CAT(0) space Moreau-Yosida resolvent Implicit iterative rule proximal point algorithm Variational inequality

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：