检索结果-内蒙古大学图书馆

SPLIT-DOUGLAS-RACHFORD ALGORITHM FOR COMPOSITE MONOTONE INCLUSIONS AND SPLIT-ADMM

SIAM JOURNAL ON OPTIMIZATION 2021年第4期31卷 2987-3013页

作者： Briceno-Arias, Luis M. Roldan, Fernando Univ Tecn Federico Santa Maria Dept Math Santiago Chile

In this paper we provide a generalization of the Douglas-Rachford splitting (DRS) and the primal-dual algorithm [L. Condat, J. Optim. Theory Appl., 158 (2013), pp. 460-479;B. C. Vu, Adv. Comput. Math., 38 (2013), pp. 667-681] for solving monotone inclusions in a real Hilbert space involving a general linear operator. The proposed method allows for primal and dual nonstandard metrics and activates the linear operator separately from the monotone operators appearing in the inclusion. In the simplest case when the linear operator has full range, it reduces to classical DRS. Moreover, the weak convergence of primal-dual sequences to a Kuhn-Tucker point is guaranteed, generalizing the main result in [B. F. Svaiter, SIAM J. Control Optim., 49 (2011), pp. 280-287]. Inspired by [D. Gabay, Applications of the method of multipliers to variational inequalities, in Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, M. Fortin and R. Glowinski, eds., Stud. Math. Appl. 15, North-Holland, Amsterdam, 1983, pp. 299-331], we also derive a new split alternating direction method of multipliers (SADMM) by applying our method to the dual of a convex optimization problem involving a linear operator which can be expressed as the composition of two linear operators. The proposed SADMM activates one linear operator implicitly and the other one explicitly, and we recover ADMM when the latter is set as the identity. Connections and comparisons of our theoretical results with respect to the literature are provided for the main algorithm and SADMM. The flexibility and efficiency of both methods is illustrated via numerical simulations in total variation image restoration and a sparse minimization problem.

关键词： ADMM convex optimization Douglas-Rachford splitting fixed point iterations monotone operator theory quasinonexpansive operators splitting algorithms

来源：评论

学校读者我要写书评

暂无评论

A Projected Primal-Dual Method for Solving Constrained Monotone Inclusions

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2019年第3期180卷 907-924页

作者： Briceno-Arias, Luis Lopez Rivera, Sergio Univ Tecn Federico Santa Maria Dept Matemat Santiago Chile

In this paper, we provide an algorithm for solving constrained composite primal-dual monotone inclusions, i.e., monotone inclusions in which a priori information on primal-dual solutions is represented via closed and convex sets. The proposed algorithm incorporates a projection step onto the a priori information sets and generalizes methods proposed in the literature for solving monotone inclusions. Moreover, under the presence of strong monotonicity, we derive an accelerated scheme inspired on the primal-dual algorithm applied to the more general context of constrained monotone inclusions. In the particular case of convex optimization, our algorithm generalizes several primal-dual optimization methods by allowing a priori information on solutions. In addition, we provide an accelerated scheme under strong convexity. An application of our approach with a priori information is constrained convex optimization problems, in which available primal-dual methods impose constraints via Lagrange multiplier updates, usually leading to slow algorithms with unfeasible primal iterates. The proposed modification forces primal iterates to satisfy a selection of constraints onto which we can project, obtaining a faster method as numerical examples exhibit. The obtained results extend and improve several results in the literature.

关键词： Accelerated schemes Constrained convex optimization Monotone operator theory Proximity operator splitting algorithms

来源：评论

学校读者我要写书评

暂无评论

ONLINE ROBUST PORTFOLIO RISK MANAGEMENT USING TOTAL LEAST-SQUARES AND PARALLEL splitting algorithms

ONLINE ROBUST PORTFOLIO RISK MANAGEMENT USING TOTAL LEAST-SQ...

引用

IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Konstantinos Slavakis Geert Leus Georgios B. Giannakis University of Minnesota Digital Technology Center Minneapolis USA Delft University of Technology Dept. of Microelectronics Delft The Netherlands

ISBN: (纸本)9781479903573

The present paper introduces a novel online asset allocation strategy which accounts for the sensitivity of Markowitz-inspired portfolios to low-quality estimates of the mean and the correlation matrix of stock returns. The proposed methodology builds upon the total least-squares (TLS) criterion regularized with sparsity attributes, and the ability to incorporate additional convex constraints on the portfolio vector. To solve such an optimization task, the present paper draws from the rich family of splitting algorithms to construct a novel online splitting algorithm with computational complexity that scales linearly with the number of unknowns. Real-world financial data are utilized to demonstrate the potential of the proposed technique.

关键词： Markowitz portfolio total least-squares sparsity splitting algorithms proximal mapping projection

来源：评论

学校读者我要写书评

暂无评论

On the Complexity of the Projective splitting and Spingarn's Methods for the Sum of Two Maximal Monotone Operators

引用

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2018年第1期178卷 153-190页

作者： Machado, Majela Penton IMPA Estr Dona Castorina 110 BR-22460320 Rio De Janeiro Brazil

In this work, we study the pointwise and ergodic iteration complexity of a family of projective splitting methods proposed by Eckstein and Svaiter, for finding a zero of the sum of two maximal monotone operators. As a consequence of the complexity analysis of the projective splitting methods, we obtain complexity bounds for the two-operator case of Spingarn's partial inverse method. We also present inexact variants of two specific instances of this family of algorithms and derive corresponding convergence rate results.

关键词： splitting algorithms Maximal monotone operators Complexity Spingarn's method

来源：评论

学校读者我要写书评

暂无评论

Palindromic 3-stage splitting integrators, a roadmap

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2017年 346卷 340-355页

作者： Campos, Cedric M. Sanz-Serna, J. M. Univ Yachay Tech Dept Matemat Hda San Jose S-N Urcuqui 100115 Ecuador Univ Carlos III Madrid Dept Matemat Ave Univ 30 E-28911 Leganes Madrid Spain Univ Valladolid Dept Matemat Aplicada Paseo Belen 7 E-47011 Valladolid Spain Univ Valladolid IMUVA Paseo Belen 7 E-47011 Valladolid Spain

The implementation of multi-stage splitting integrators is essentially the same as the implementation of the familiar Strang/Verlet method. Therefore multi-stage formulas may be easily incorporated into software that now uses the Strang/Verlet integrator. We study in detail the two-parameter family of palindromic, three-stage splitting formulas and identify choices of parameters that may outperform the Strang/Verlet method. One of these choices leads to a method of effective order four suitable to integrate in time some partial differential equations. Other choices may be seen as perturbations of the Strang method that increase efficiency in molecular dynamics simulations and in Hybrid Monte Carlo sampling. (C) 2017 Elsevier Inc. All rights reserved.

关键词： splitting algorithms Verlet integrator Molecular dynamics Partial differential equations Hamiltonian Monte Carlo

来源：评论

学校读者我要写书评

暂无评论

Word Series for Dynamical Systems and Their Numerical Integrators

引用

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2017年第3期17卷 675-712页

作者： Murua, A. Sanz-Serna, J. M. Univ Basque Country Informatika Fak Konputazio Zientziak & AA Saila Donostia San Sebastian 20018 Spain Univ Carlos III Madrid Dept Matemat Ave Univ 30 Madrid 28911 Spain

We study word series and extended word series, classes of formal series for the analysis of some dynamical systems and their discretizations. These series are similar to but more compact than B-series. They may be composed among themselves by means of a simple rule. While word series have appeared before in the literature, extended word series are introduced in this paper. We exemplify the use of extended word series by studying the reduction to normal form and averaging of some perturbed integrable problems. We also provide a detailed analysis of the behavior of splitting numerical methods for those problems.

关键词： Word series Hopf algebras Hamiltonian problems Normal forms Averaging splitting algorithms

来源：评论

学校读者我要写书评

暂无评论

New splitting algorithms for geometric transformations of digital images and their error analysis

引用

INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY 2011年第4期21卷 323-335页

作者： Li, Zi-Cai Chiang, John Y. Suen, C. Y. Natl Sun Yat Sen Univ Dept Comp Sci & Engn Kaohsiung 80424 Taiwan Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung 80424 Taiwan Concordia Univ Ctr Pattern Recognit & Machine Intelligence Montreal PQ H3G 1M8 Canada

For digital images and patterns under the nonlinear geometric transformation, T: (xi, eta) > (x, y), this study develops the splitting algorithms (i.e., the pixel-division algorithms) that divide a 2D pixel into N x N subpixels, where N is a positive integer chosen as N = 2(k)(k >= 0) in practical computations. When the true intensity values of pixels are known, this method makes it easy to compute the true intensity errors. As true intensity values are often unknown, the proposed approaches can compute the sequential intensity errors based on the differences between the two approximate intensity values at N and N/2. This article proposes the new splittingshooting method, new splitting integrating method, and their combination. These methods approximate results show that the true errors of pixel intensity are O(H), where H is the pixel size. Note that the algorithms in this article do not produce any sequential errors as N >= N(0), where N(0) (>= 2) is an integer independent of N and H. This is a distinctive feature compared to our previous papers on this subject. The other distinct feature of this article is that the true error bound O(H) is well suited to images with all kinds of discontinuous intensity, including scattered pixels. (C) 2011 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 21, 323335, 2011

关键词： image geometric transformation digital images splitting algorithms splitting-shooting method error analysis

来源：评论

学校读者我要写书评

暂无评论

splitting K-symplectic methods for non-canonical separable Hamiltonian problems

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2016年第0期322卷 387-399页

作者： Zhu, Beibei Zhang, Ruili Tang, Yifa Tu, Xiongbiao Zhao, Yue Chinese Acad Sci Acad Math & Syst Sci ICMSEC LSEC Beijing 100190 Peoples R China Univ Sci & Technol China Ctr Adv Fus Energy & Plasma Sci Dept Modern Phys & Collaborat Innovat Hefei 230026 Anhui Peoples R China

Non-canonical Hamiltonian systems have K-symplectic structures which are preserved by K-symplectic numerical integrators. There is no universal method to construct K-symplectic integrators for arbitrary non-canonical Hamiltonian systems. However, in many cases of interest, by using splitting, we can construct explicit K-symplectic methods for separable non-canonical systems. In this paper, we identify situations where splitting K-symplectic methods can be constructed. Comparative numerical experiments in three non-canonical Hamiltonian problems show that symmetric/non-symmetric splitting K-symplectic methods applied to the non-canonical systems are more efficient than the same-order Gauss' methods/non-symmetric symplectic methods applied to the corresponding canonicalized systems;for the non-canonical Lotka-Volterra model, the splitting algorithms behave better in efficiency and energy conservation than the K-symplectic method we construct via generating function technique. In our numerical experiments, the favorable energy conservation property of the splitting K-symplectic methods is apparent. (C) 2016 Elsevier Inc. All rights reserved.

关键词： K-symplectic methods splitting algorithms Gauss' methods Generating function methods

来源：评论

学校读者我要写书评

暂无评论

A TECHNIQUE FOR STUDYING STRONG AND WEAK LOCAL ERRORS OF splitting STOCHASTIC INTEGRATORS

引用

SIAM JOURNAL ON NUMERICAL ANALYSIS 2016年第6期54卷 3239-3257页

作者： Alamo, A. Sanz-Serna, J. M. Univ Valladolid Fac Ciencias Dept Matemat Aplicada E-47011 Valladolid Spain Univ Valladolid Fac Ciencias IMUVA E-47011 Valladolid Spain Univ Carlos III Madrid Dept Matemat Ave Univ 30 E-28911 Madrid Spain

We present a technique, based on so-called word series, to write down in a systematic way expansions of the strong and weak local errors of splitting algorithms for the integration of Stratonovich stochastic differential equations. Those expansions immediately lead to the corresponding order conditions. Word series are similar to, but simpler than, the B-series used to analyze Runge-Kutta and other one-step integrators. The suggested approach makes it unnecessary to use the Baker-Campbell-Hausdorff formula. As an application, we compare two splitting algorithms recently considered by Leimkuhler and Matthews to integrate the Langevin equations. The word series method clearly bears out reasons for the advantages of one algorithm over the other.

关键词： stochastic differential equations splitting algorithms Langevin equations word series

来源：评论

学校读者我要写书评

暂无评论

A bundle method using two polyhedral approximations of the ε-enlargement of a maximal monotone operator

引用

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2016年第1期64卷 75-100页

作者： Nagesseur, Ludovic Univ Antilles LAMIA F-97159 Pointe A Pitre Guadeloupe France

Until now, a few bundle methods for general maximal monotone operators exist and they were only employed with one polyhedral approximation of the -enlargement of the maximal monotone operator considered. However, we find in the literature several hybrid-proximal methods which could be adapted with a great deal of bundle techniques in order to find a zero of a maximal monotone operator;yet, we could also consider the use of two polyhedral approximations. The method developed in this study has used a double polyhedral approximation at each iteration. Besides, as an application, we give a bundle method for a forward-backward type algorithm.

关键词： Maximal monotone operator epsilon-Enlargement Proximal point algorithm splitting algorithms Bundle methods

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：