检索结果-南通市图书馆

A superlinear convergence scheme for nonlinear fractional differential equations and its fast implement

在线全文

学校读者我要写书评

暂无评论

International Journal of Modeling, Simulation, and Scientific Computing 2019年第1期10卷 1-16页

作者： Haobo Gong Jingna Zhang Hao Guo Jianfei Huang College of Mathematical Sciences Yangzhou University Yangzhou 225002P.R.China

In this paper,we first construct an efficient scheme for nonlinear Caputo fractional differential equations with the initial value and the fractional degree 0<α<***,the unconditional stability and the superlinear con... 详细信息

In this paper,we first construct an efficient scheme for nonlinear Caputo fractional differential equations with the initial value and the fractional degree 0superlinear convergence with the order 1+αof the proposed scheme are strictly proved and *** to the nonlocal property of fractional operators,the new scheme is time-consuming for long-time ***,a fast implement of the proposed scheme is presented based on the sum-of-exponentials(SOE)approximation for the kernel tα−1 on the interval[h,T]in the Riemann-Liouville integral,where h is the *** numerical experiments are provided to support the theoretical results of the new scheme and demonstrate the computational performance of its fast implement.

关键词： Fractional differential equations nonlinear system stability superlinear convergence fast implement

Optimization methods rooted in optimal control

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Science China(Information Sciences) 2024年第12期67卷 272-280页

作者： Huanshui ZHANG Hongxia WANG Yeming XU Ziyuan GUO School of Electrical and Automation Engineering Shandong University of Science and Technology School of Control Science and Engineering Shandong University

In the paper, we investigate the optimization problem(OP) by applying the optimal control method. The optimization problem is reformulated as an optimal control problem(OCP) where the controller(iteration updating) is designed to minimize the sum of costs in the future time instant, which thus theoretically generates the “optimal algorithm”(fastest and most stable). By adopting the maximum principle and linearization with Taylor expansion, new algorithms are proposed. It is shown that the proposed algorithms have a superlinear convergence rate and thus converge more rapidly than the gradient descent;meanwhile, they are superior to Newton's method because they are not divergent in general and can be applied in the case of a singular or indefinite Hessian matrix. More importantly, the OCP method contains the gradient descent and the Newton's method as special cases, which discovers the theoretical basis of gradient descent and Newton's method and reveals how far these algorithms are from the optimal algorithm. The merits of the proposed optimization algorithm are illustrated by numerical experiments.

关键词： optimal control optimization methods optimization algorithm maximum principle superlinear convergence

同方期刊数据库

SINGLY DIAGONALLY IMPLICIT RUNGE-KUTTA METHODS COMBINING LINE SEARCH TECHNIQUES FOR UNCONSTRAINED OPTIMIZATION

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2005年第2期23卷 153-164页

作者： Xin-longLuo SchoolofInformationEngineering BeijingUniversityofPostsandTelecommunicationsP.O.Box101Beijing100876China

There exists a strong connection between numerical methods for the integration of ordinary differential equations and optimization problems. In this paper, we try to discover further their links. And we transform unconstrained problems to the equivalent ordinary differential equations and construct the LRKOPT method to solve them by combining the second order singly diagonally implicit Runge-Kutta formulas and line search *** we analyze the global convergence and the local convergence of the LRKOPT method. Promising numerical results are also reported.

关键词： Global convergence superlinear convergence Runge-Kutta method Unconstrained optimization

THE convergence OF A NEW MODIFIED BFGS METHOD WITHOUT LINE SEARCHES FOR UNCONSTRAINED OPTIMIZATION OR COMPLEXITY SYSTEMS

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 Systems Science & Complexity 2010年第4期23卷 861-872页

作者： Liying LIU Zengxin WEI Xiaoping WU College of Mathematics Science Liaocheng University Liaocheng 252059 China College of Mathematics and Information Science Guangxi University Nanning 530004 China School of Management Xi'an Jiaotong University Xi'an 710049 China

In this paper,a new modified BFGS method without line searches is *** traditionalBFGS method,this modified BFGS method is proposed based on the so-called fixed steplengthstrategy introduced by Sun and *** some suitable assumptions,the global convergence andthe superlinear convergence of the new algorithm are established,*** some preliminarynumerical experiments,which shows that the new Algorithm is feasible,is also reported.

关键词： BFGS method complexity systems global convergence superlinear convergence unconstrained optimization.

A TRULY GLOBALLY CONVERGENT FEASIBLE NEWTON-TYPE METHOD FOR MIXED COMPLEMENTARITY PROBLEMS

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2004年第3期22卷 347-360页

作者： DerenHan SchoolofMathematicsandComputerScience NanjingNormalUniversityNanjing210097China

Typical solution methods for solving mixed complementarity problems either generate feasible iterates but have to solve relatively complicated subproblems such as quadratic programs or linear complementarity problems, or (those methods) have relatively simple subproblems such as system of linear equations but possibly generate infeasible *** this paper, we propose a new Newton-type method for solving monotone mixed complementarity problems, which ensures to generate feasible iterates, and only has to solve a system of well-conditioned linear equations with reduced dimension per iteration. Without any regularity assumption, we prove that the whole sequence of iterates converges to a solution of the problem (truly globally convergent). Furthermore, under suitable conditions,the local superlinear rate of convergence is also established.

关键词： Mixed complementarity problems Newton-type methods Global convergence superlinear convergence

convergence PROPERTIES OF A MODIFIED BFGSALGORITHM FOR MINIMIZATION WITHARMIJO-GOLDSTEIN STEPLENGTHS

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 Computational Mathematics 1999年第6期17卷 645-652页

作者： Nai-yang Deng Zheng-feng Li(Department of Mathematics, Beijing Agricultural Engineering University, Beijing 100083,China) 北京农业工程大学数学系北京 100083 北京农业工程大学数学系北京

The line search strategy is crucial for an efficient unconstrained optimization algorithm. One of the reason why the Wolfe line searches is recommended lies in that it ensures positive definiteness of BFGS updates. When gradient information has to be obtained costly, the Armijo-Goldstein line searches may be preferred. To maintain positive difiniteness of BFGS updates based on the Armijo-Goldstein line searches, a slightly modified form of BFGS update is proposed by I.D. Coope and C.J. Price (Journal of Computational Mathematics, 13 (1995), 156-160), while its convergence properties is open up to now. This paper shows that the modified BFGS algorithm is globally and superlinearly convergent based on the Armijo-Goldstein line searches.

关键词： BFGS methods convergence superlinear convergence

convergence PROPERTIES OF MULTI-DIRECTIONAL PARALLEL ALGORITHMS FOR UNCONSTRAINED MINIMIZATION

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2005年第4期23卷 357-372页

作者： Cheng-xian Xu Yue-ting Yang Faculty of Sciences Xi'an Jiaotong University Xi'an 710049 China

convergence properties of a class of multi-directional parallel quasi-Newton algorithms for the solution of unconstrained minimization problems are studied in this paper. At each iteration these algorithms generate several different quasi-Newton directions, and then apply line searches to determine step lengths along each direction, simultaneously. The next iterate is obtained among these trail points by choosing the lowest point in the sense of function reductions. Different quasi-Newton updating formulas from the Broyden family are used to generate a main sequence of Hessian matrix approximations. Based on the BFGS and the modified BFGS updating formulas, the global and superlinear convergence results are proved. It is observed that all the quasi-Newton directions asymptotically approach the Newton direction in both direction and length when the iterate sequence converges to a local minimum of the objective function, and hence the result of superlinear convergence follows.

关键词： Unconstrained minimization Multi-directional parallel quasi-Newton method Global convergece superlinear convergence

A New superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems

在线全文

维普期刊数据库

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 REVISED CONJUGATE GRADIENT PROJECTION ALGORITHM FOR INEQUALITY CONSTRAINED OPTIMIZATIONS

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2005年第2期23卷 217-224页

作者： WeiWang Lian-shengZhang Yi-fanXu DepartmentofAppliedMathematics TongjiUniversityShanghai200092China//DepartmentofMathematicsShanghaiUniversityShanghai200436China DepartmentofMathematics ShanghaiUniversityShanghai200436China SchoolofManagement FudanUniversityShanghai200433China

A revised conjugate gradient projection method for nonlinear inequality constrained optimization problems is proposed in the paper, since the search direction is the combination of the conjugate projection gradient and the quasi-Newton direction. It has two merits. The one is that the amount of computation is lower because the gradient matrix only needs to be computed one time at each iteration. The other is that the algorithm is of global convergence and locally superlinear convergence without strict complementary condition under some mild assumptions. In addition the search direction is explicit.

关键词： Constrained optimization Conjugate gradient projection Revised direction superlinear convergence