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1.
本文将文[1]提出的一类求总极值方法与非线性规划的下降方法相结合,提出一类带下降方向搜索的求总极值方法,并且证明了这类方法具有线性和超线性收效率.  相似文献   

2.
无重复试验的饱和设计可节省大量的试验时间和费用,带来较大的经济效益,饱和析因设计在实际应用中使用越来越多.但以往统计工作者大部分都是在试验响应变量服从连续分布(如正态分布,t分布,指数分布,Weibull分布等)和Pareto效应稀疏条件下研究的,一直以来还没有人对试验响应变量服从离散分布饱和析因设计进行过研究.本文就...  相似文献   

3.
针对遗传算法爬山能力弱但合局搜索能力强的特点 ,本文将遗传算法嵌入到基入传统优化的拟下降算法中 ,并对算法的拟下降步骤做了一定的改进 ,使得整个算法具有全局收敛性 .本文采用马尔可夫的观点进一步证明了算法的全局收敛性 ,并用极难优化的测试函数给出了数值算例 ,证明了本文算法为一种可行的全局优化算法 .  相似文献   

4.
提出了一种三项超记忆梯度方法.该方法的最大优点是:在无需线性搜索的条件下,迭代方向就是充分下降方向.在较弱的条件下,分析了方法的全局收敛性.初步数值试验表明方法是有效的.  相似文献   

5.
本指出了[4]的一个错误。用最速下降规则,给出了选择割平面的一个新方法。一个复杂的例子说明,该方法有一定的实用价值。  相似文献   

6.
本本文给出了一个解非线性对称方程组问题的具有下降方向的近似高斯一牛顿基础BFGS方法。无论使用何种线性搜索此方法产生的方向总是下降的。在适当的条件下我们将证明此方法的全局收敛性和超线性收敛性。并给出数值检验结果。  相似文献   

7.
王开荣  张杨 《应用数学》2012,25(3):515-526
我们基于拟牛顿法的割线条件提出两种LS型共轭梯度法.有趣的是,我们提出的方法中对于βk的计算公式与戴和廖[3]提出的有相似的结构.但是,新方法能够在合理的假设下保证充分下降性,这一点是戴-廖方法所不具备的.在强Wolfe线搜索下,给出了新方法的全局收敛结果.数值结果论证了该方法的有效性.  相似文献   

8.
本文讨论了共轭下降法的全局收敛性,对于共轭下降法,建立了两个新的全局收敛性结果,这些结果是文(1)结果的推广。  相似文献   

9.
一种无约束全局优化的水平值下降算法   总被引:1,自引:0,他引:1  
彭拯  张海东  邬冬华 《应用数学》2007,20(1):213-219
本文研究无约束全局优化问题,建立了一种新的水平值下降算法(Level-value Descent Method,LDM).讨论并建立了概率意义下取全局最小值的一个充分必要条件,证明了算法LDM是依概率测度收敛的.这种LDM算法是基于重点度取样(Improtance Sampling)和Markov链Monte-Carlo随机模拟实现的,并利用相对熵方法(TheCross-Entropy Method)自动更新取样密度,算例表明LDM算法具有较高的数值精度和较好的全局收敛性.  相似文献   

10.
共轭下降法的全局收敛性   总被引:22,自引:1,他引:21  
袁亚湘 《数学进展》1996,25(6):552-562
共轭下降法最早由Fletcher提出,本文证明了一类非精确线搜索条件能保证共轭下的降法的收敛性,并且构造了反例表明,如果线搜索条件放松,则共轭下降法可能不收敛,此外,我们还得到了与Flecher-Reeves方法有关的一类方法的结论。  相似文献   

11.
王继强 《大学数学》2004,20(6):44-46
分析了大M法与两阶段法在思想方法、辅助线性规划问题的构造、初始可行基、初始单纯形表、最优性检验和算法步骤等方面的一致性.  相似文献   

12.
In the framework of Symmetric Galerkin Boundary Element Method, different techniques in these last years have been proposed to reduce the computational cost of the Galerkin matrix evaluation: in particular, the Panel Clustering Method [25,26] it is now largely used. On the other side, very recently a theory on restriction matrices has been developed to take computational advantage of possible symmetry properties of the differential or integral problem at hand [4,5]. Here we couple Panel Clustering Method with restriction matrices, presenting the most important algorithms employed and showing several examples, comparisons and numerical results. AMS subject classification 65F30, 65N38  相似文献   

13.
In this article, we consider a variant of the Dual Reciprocity Method (DRM) for solving boundary value problems based on approximating source terms by polynomials other than the traditional basis functions. The use of pseudo‐spectral approximations and symbolic methods enables us to obtain highly accurate results without solving the often ill‐conditioned equations that occur when radial basis function approximations are used. When the given partial differential equation is either Poisson's equation or an inhomogeneous Helmholtz‐type equation, we are able to obtain either closed form particular solutions or efficient recursive algorithms. Using the particular solutions, we convert the inhomogeneous equations to homogeneous. The resulting homogeneous equations are then amenable to solution by boundary‐type methods such as the Boundary Element Method (BEM) or the Method of Fundamental Solutions (MFS). Using the MFS, we provide numerical solutions to a variety of boundary value problems in R2 and R3 . Using this approach, we can achieve high accuracy with a modest number of interpolation and collocation points. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 112–133, 2003  相似文献   

14.
1.引言 为提高用数值方法解非线性发展方程及非线性椭圆边值问题的逼近阶,许多学者例如J.Novo和 E.Titi[4], Marion和 Teman[6],J.Xu[7]以及 W.Layton[9]等人,提出了后验Galerkin方法、近似惯性流形方法、非线性Galerkin方法、各种区域分裂法、多重网格法等等.本文根据[1]提出了一种新的高精度的后验 Galerkin方法.它的逼近阶是经典 Galerkin方法逼近阶的两倍. 考虑非线性椭圆边值问题这里n是按d=2,3)上具有分段光滑边界r的有界区域,…  相似文献   

15.
The accuracy of a finite element numerical approximation of the solution of a partial differential equation can be spoiled significantly by singularities. This phenomenon is especially critical for high order methods. In this paper, we show that, if the PDE is linear and the singular basis functions are homogeneous solutions of the PDE, the augmentation of the trial function space for the Finite Volume Element Method (FVEM) can be done significantly simpler than for the Finite Element Method. When the trial function space is augmented for the FVEM, all the entries in the matrix originating from the singular basis functions in the discrete form of the PDE are zero, and the singular basis functions only appear in the boundary conditions. That is to say, there is no need to integrate the singular basis functions over the elements and the sparsity of the matrix is preserved without special care. FVEM numerical convergence studies on two-dimensional triangular grids are presented using basis functions of arbitrary high order, confirming the same order of convergence for singular solutions as for smooth solutions.  相似文献   

16.
李慧茹 《经济数学》2002,19(1):85-94
通过定义一种新的*-微分,本文给出了局部Lipschitz非光滑方程组的牛顿法,并对其全局收敛性进行了研究.该牛顿法结合了非光滑方程组的局部收敛性和全局收敛性.最后,我们把这种牛顿法应用到非光滑函数的光滑复合方程组问题上,得到了较好的收敛性.  相似文献   

17.
In this work, we study the application of the Method of Fundamental Solutions (MFS) for the calculation of eigenfrequencies and eigenmodes in two and three‐dimensional domains. We address some mathematical results about properties of the single layer operator related to the eigenfrequencies. Moreover, we propose algorithms for the distribution of the collocation and source points of the MFS in three‐dimensional domains which is an extension of the choices considered by Alves and Antunes (CMC 2(2005), 251–266) for the two‐dimensional case. Also the application of the Plane Waves Method is investigated. Several examples with Dirichlet and Neumann boundary conditions are considered to illustrate the performance of the proposed methods. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1525–1550, 2011  相似文献   

18.
The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we propose an efficient algorithm for the linear least-squares version of the MFS, when applied to the Dirichlet problem for certain second order elliptic equations in a disk. Various aspects of the method are discussed and a comparison with the standard MFS is carried out. Numerical results are presented.  相似文献   

19.
In this paper we propose an exact method able to solve multi-objective combinatorial optimization problems. This method is an extension, for any number of objectives, of the 2-Parallel Partitioning Method (2-PPM) we previously proposed. Like 2-PPM, this method is based on splitting of the search space into several areas, leading to elementary searches. The efficiency of the proposed method is evaluated using a multi-objective flow-shop problem.  相似文献   

20.
In this research paper, we examine a novel method called the Natural Decomposition Method (NDM). We use the NDM to obtain exact solutions for three different types of nonlinear ordinary differential equations (NLODEs). The NDM is based on the Natural transform method (NTM) and the Adomian decomposition method (ADM). By using the new method, we successfully handle some class of nonlinear ordinary differential equations in a simple and elegant way. The proposed method gives exact solutions in the form of a rapid convergence series. Hence, the Natural Decomposition Method (NDM) is an excellent mathematical tool for solving linear and nonlinear differential equation. One can conclude that the NDM is efficient and easy to use.  相似文献   

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