检索结果-内蒙古大学图书馆

A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques

Chinese Annals of Mathematics,Series B 2023年第5期44卷 719-734页

作者： Pengcheng XIE Ya-xiang YUAN State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematicsand Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesUniversity of Chinese Academy of SciencesBeijing 100190China

The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration *** analyze the optimization dynamics and convergence of the algorithm *** of the trial step and structure step are *** results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD *** algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.

关键词： Nonlinear optimization Derivative-Free Quadratic model Line-Search Trust-Region

来源：评论

学校读者我要写书评

暂无评论

Adaptive cyclic gradient methods with interpolation

引用

Computational Optimization and Applications 2025年 1-25页

作者： Xie, Yixin Sun, Cong Yuan, Ya-Xiang Beijing100876 China Ministry of Education Beijing100876 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

Gradient method is an important method for solving large scale problems. In this paper, a new gradient method framework for unconstrained optimization problem is proposed, where the stepsize is updated in a cyclic way. The Cauchy step is approximated by the quadratic interpolation. And the cycle for stepsize update is adjusted adaptively. Combining with the adaptive nonmonotone line search technique, we prove the global convergence of the proposed method. Furthermore, its sublinear convergence rate for convex problems and R-linear convergence rate for problems with quadratic functional growth property are analyzed. Numerical results show that our proposed algorithm enjoys good performances in terms of both computational cost and obtained function values. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： Interpolation

来源：评论

学校读者我要写书评

暂无评论

On greedy randomized coordinate updating iteration methods for solving symmetric eigenvalue problems

引用

Applied Numerical Mathematics 2025年 216卷 76-97页

作者： Bai, Zhong-Zhi State Key Laboratory of Mathematical Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences P.O. Box 2719 Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In order to compute the smallest eigenvalue and its corresponding eigenvector of a large-scale, real, and symmetric matrix, we propose a class of greedy randomized coordinate updating iteration methods based on the principle that the indices of larger entries in absolute value of the current residual are selected with a higher probability and, with respect to this index set, the next iterate is updated from the current iterate along with the selected coordinate such that the corresponding entry of the residual is annihilated, resulting in fast convergence rates of the proposed iteration methods. Under appropriate conditions, we prove the convergence of both sequences of the Rayleigh-quotients and the acute angles between the iterates and the eigenvector in terms of the expectation. By numerical experiments, we show that this class of greedy randomized coordinate updating iteration methods are advantageous over the parameterized power method and the coordinate descent method in both iteration counts and computing times. Moreover, with theoretical analysis and computational performance, we confirm that the convergence property of this class of iteration methods can be improved significantly by suitably choosing the arbitrary nonnegative parameter involved in the greedy probability criterion. © 2025 IMACS

关键词： Eigenvalues and eigenfunctions

来源：评论

学校读者我要写书评

暂无评论

SOLVING OPTIMIZATION PROBLEMS OVER THE STIEFEL MANIFOLD BY SMOOTH EXACT PENALTY FUNCTIONS

引用

Journal of Computational Mathematics 2024年第5期42卷 1246-1276页

作者： Nachuan Xiao Xin Liu The Institute of Operations Research and Analytics National University of SingaporeSingapore State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of Sciencesand University of Chinese Academy of SciencesChina

In this paper,we present a novel penalty model called ExPen for optimization over the Stiefel *** from existing penalty functions for orthogonality constraints,ExPen adopts a smooth penalty function without using any first-order derivative of the objective *** show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible,namely,are the first-order stationary points of the original optimization problem,or far from the Stiefel ***,the original problem and ExPen share the same second-order stationary ***,the exact gradient and Hessian of ExPen are easy to *** a consequence,abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.

关键词： Orthogonality constraint Stiefel manifold Penalty function

来源：评论

学校读者我要写书评

暂无评论

Multiscale method for identifying and marking the multiform fractures from visible-light rock-mass images

引用

Underground Space 2024年第3期16卷 279-300页

作者： Yongbo Pan Junzhi Cui Zhenhao Xu School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China The State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China Geotechnical and Structural Engineering Research Center Shandong UniversityJinan 250100China

Multiform fractures have a direct impact on the mechanical performance of rock *** accurately identify multiform fractures,the distribution patterns of grayscale and the differential features of fractures in their neighborhoods are *** on this,a multiscale processing algorithm is *** multiscale process is as *** the neighborhood of pixels,a grayscale continuous function is constructed using bilinear interpolation,the smoothing of the grayscale function is realized by Gaussian local filtering,and the grayscale gradient and Hessian matrix are calculated with high *** small-scale blocks,the pixels are classified by adaptively setting the grayscale threshold to identify potential line segments and *** the global image,potential line segments and mini-fillings are spliced together by progressing the block frontier layer-by-layer to identify and mark multiform *** accuracy of identifying multiform fractures is improved by constructing a grayscale continuous function and adaptively setting the grayscale thresholds on small-scale *** the layer-by-layer splicing algorithm is performed only on the domain of the 2-layer small-scale blocks,reducing the *** using rock mass images with different fracture types as examples,the identification results show that the proposed algorithm can accurately identify the multiform fractures,which lays the foundation for calculating the mechanical parameters of rock masses.

关键词： Visible light rock-mass images Continuous grayscale function Small-scale blocks Multiform fractures

来源：评论

学校读者我要写书评

暂无评论

The exactness of the l_(1)penalty function for a class of mathematical programs with generalized complementarity constraints

引用

Fundamental Research 2024年第6期4卷 1459-1464页

作者： Yukuan Hu Xin Liu State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

In a mathematical program with generalized complementarity constraints(MPGCC),complementarity relation is imposed between each pair of variable *** includes the traditional mathematical program with complementarity constraints(MPCC)as a special *** account of the disjunctive feasible region,MPCC and MPGCC are generally difficult to *** l_(1)penalty method,often adopted in computation,opens a way of circumventing the *** it remains unclear about the exactness of the l_(1)penalty function,namely,whether there exists a sufficiently large penalty parameter so that the penalty problem shares the optimal solution set with the original *** this paper,we consider a class of MPGCCs that are of multi-affine objective *** problem class finds applications in various fields,e.g.,the multi-marginal optimal transport problems in many-body quantum physics and the pricing problems in network *** first provide an instance from this class,the exactness of whose l_(1)penalty function cannot be derived by existing *** then establish the exactness results under rather mild *** results cover those existing ones for MPCC and apply to multi-block contexts.

关键词： Mathematical program with generalized complementarity constraints l_(1)penalty function Exact penalty Multi-affine objective function Error bound

来源：评论

学校读者我要写书评

暂无评论

The convergence properties of infeasible inexact proximal alternating linearized minimization

引用

Science China Mathematics 2023年第10期66卷 2385-2410页

作者： Yukuan Hu Xin Liu State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real *** the cases where subproblems do not have closed-form solutions,e.g.,due to complex constraints,infeasible subsolvers are indispensable,giving rise to an infeasible inexact PALM(PALM-I).Numerous efforts have been devoted to analyzing the feasible PALM,while little attention has been paid to the *** usage of the PALM-I thus lacks a theoretical *** essential difficulty of analysis consists in the objective value nonmonotonicity induced by the *** study in the present work the convergence properties of the *** particular,we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact *** upon these,we manage to establish the stationarity of any accumulation point,and moreover,show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz *** prominent advantages of the PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3-dimensional anisotropic frictional contact.

关键词： proximal alternating linearized minimization infeasibility nonmonotonicity surrogate sequence inexact criterion iterate convergence asymptotic convergence rate

来源：评论

学校读者我要写书评

暂无评论

STOCHASTIC TRUST-REGION METHODS WITH TRUST-REGION RADIUS DEPENDING ON PROBABILISTIC MODELS

引用

Journal of Computational Mathematics 2022年第2期40卷 294-334页

作者： Xiaoyu Wang Ya-xiang Yuan Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic ***,we propose a specific algorithm termed STRME,in which the trust-region radius depends linearly on the gradient used to define the latest *** complexity results of the STRME method in nonconvex,convex and strongly convex settings are presented,which match those of the existing algorithms based on probabilistic *** addition,several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient methods.

关键词： Trust-region methods,Stochastic optimization Probabilistic models Trust-region radius Global convergence

来源：评论

学校读者我要写书评

暂无评论

A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

引用

Communications on Applied Mathematics and Computation 2023年第1期5卷 3-30页

作者： Kunlei Zhao Yulong Du Li Yuan State Key Laboratory of Scientific and Engineering Computing(LSEC)and Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences Beihang UniversityBeijing 100191China

In this paper,we develop a new sixth-order WENO scheme by adopting a convex combina-tion of a sixth-order global reconstruction and four low-order local *** the classical WENO schemes,the associated linear weights of the new scheme can be any positive numbers with the only requirement that their sum equals ***,a very simple smoothness indicator for the global stencil is *** new scheme can achieve sixth-order accuracy in smooth *** tests in some one-and two-dimensional bench-mark problems show that the new scheme has a little bit higher resolution compared with the recently developed sixth-order WENO-Z6 scheme,and it is more efficient than the classical fifth-order WENO-JS5 scheme and the recently developed sixth-order WENO6-S scheme.

关键词： Global smoothness indicator Linear weights Sixth-order accuracy WENO

来源：评论

学校读者我要写书评

暂无评论

A Riemannian Exponential Augmented Lagrangian Method for computing the Projection Robust Wasserstein Distance 37

A Riemannian Exponential Augmented Lagrangian Method for Com...

引用

37th Conference on Neural Information Processing Systems, NeurIPS 2023

作者： Jiang, Bo Liu, Ya-Feng Ministry of Education Key Laboratory of NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing210023 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

ISBN: (纸本)9781713899921

Projection robust Wasserstein (PRW) distance is recently proposed to efficiently mitigate the curse of dimensionality in the classical Wasserstein distance. In this paper, by equivalently reformulating the computation of the PRW distance as an optimization problem over the Cartesian product of the Stiefel manifold and the Euclidean space with additional nonlinear inequality constraints, we propose a Riemannian exponential augmented Lagrangian method (REALM) for solving this problem. Compared with the existing Riemannian exponential penalty-based approaches, REALM can potentially avoid too small penalty parameters and exhibit more stable numerical performance. To solve the subproblems in REALM efficiently, we design an inexact Riemannian Barzilai-Borwein method with Sinkhorn iteration (iRBBS), which selects the stepsizes adaptively rather than tuning the stepsizes in efforts as done in the existing methods. We show that iRBBS can return an Ε-stationary point of the original PRW distance problem within O(Ε-3) iterations, which matches the best known iteration complexity result. Extensive numerical results demonstrate that our proposed methods outperform the state-of-the-art solvers for computing the PRW distance. © 2023 Neural information processing systems foundation. All rights reserved.

关键词： Constrained 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：