一个新的填充函数

填充函数法是一种解无约束全局极小化问题的方法.这种方法的关键是构造填充函数,在已发表的文献中已经介绍了几种填充函数.在此介绍只含一个参数的填充函数,并且根据此填充函数提出了一种填充函数算法.给出了用这种填充函数法解几个测试问题的计算结果.     

等腰三角形Mindlin板的自由振动分析

提出了一种新方法来对基于 Mindlin剪切变形理论的等腰三角形板进行自由振动分析 .此方法采用了一种新的基函数并利用 pb-2 Rayleigh-Ritz边界函数得到了一种新型的 Ritz方法 .这种方法的有效性通过收敛性和对比性分析得到了证实 .数值结果表明此方法相当精确有效 .     

关于叶果洛夫定理证明的一个注记

给出了一种函数列收敛的等价刻画,并利用此等价刻画来给出实变函数中叶果洛夫定理的另一种证明方法.     

不动点迭代法的一点注记

对于迭代函数不满足收敛定理假定条件的情况 ,提出了一种简单方法 .此方法对于迭代函数满足收敛定理假定条件的情况 ,可以加速序列收敛 .最后给出了实例和程序 .     

求全局最优化问题的一种新定义的填充函数

提出了一种新的填充函数定义和填充函数,这种填充函数只含有一个参数且可以用来寻找全局优化问题的最优点.经过理论分析提出了一种新的填充函数算法.数值实验验证了此算法的有效性.     

一种直觉模糊多属性群决策方法及其在群决策中的应用

对以直觉模糊数形式表示的信息和属性权重完全未知的多属性群决策问题进行了研究.提出了一种基于熵值的直觉模糊数距离测度方法,同时对传统的比较得分函数和精确函数的直觉模糊数排序方法进行了改进,定义了一种新的排序公式;进而利用此距离度量公式,引入到基于直觉模糊数之间距离的离差最大化方法中,确定属性的权重,提出了一种基于属性权重完全未知的直觉模糊多属性群决策方法.最后,将此方法运用在ERP选型中.     

一种模糊模式识别新方法及其在脑电图信号识别中的应用

本文给出一种确定模糊子集隶属函数的新方法——STF 隶属函数确定法.该法将随机性与模糊性联系起来,使得对相当广泛的一类问题,可借助数理统计方法确定模糊概念的隶属函数.本文还给出一种从一个模糊概念的不同方面综合考察该模糊概念的方法.提出了隶属优势的概念,在此基础上给出了一种模糊模式识别的新方法——最大隶属优势准则模式识别法.应用这种方法对137例脑电图进行了计算机识别,得到了较好的效果.     

基于g函数的多元copula的构造

针对目前多元copula的构造方法存在的局限性,提出了构造多元copula的新方法.本文首先定义的一类新的函数-g函数,基于g函数建立了2-copula的构造方法,并讨论了该方法的存在性与唯一性问题,然后将2-copula的构造方法直接扩展到n-copula构造的情形.最后给出了g函数的一种寻求方法,从而说明此copula构造方法的可行性.     

基于模块脉冲函数的非线性随机It?-Volterra积分方程数值解（英文）

为求解非线性随机It?o-Volterra积分方程,本文介绍了一种基于模块脉冲函数的有效数值方法.运用模块脉冲函数的积分算子矩阵将非线性随机积分方程转化为代数方程.通过误差分析,证明该方法收敛速度良好.最后,利用实例验证了此方法的有效性.     

基于模块脉冲函数的非线性随机It\^{o}-Volterra积分方程数值解[英文]

为求解非线性随机It\^{o}-Volterra积分方程, 本文介绍了一种基于模块脉冲函数的有效数值方法. 运用模块脉冲函数的积分算子矩阵将非线性随机积分方程转化为代数方程. 通过误差分析, 证明该方法收敛速度良好. 最后, 利用实例验证了此方法的有效性.     

A globally convergent constrained quasi-Newton method with an augmented lagrangian type penalty function

The recently proposed quasi-Newton method for constrained optimization has very attractive local convergence properties. To force global convergnce of the method, a descent method which uses Zangwill's penalty function and an exact line search has been proposed by Han. In this paper a new method which adopts a differentiable penalty function and an approximate line is presented. The proposed penalty function has the form of the augmented Lagrangian function. An algorithm for updating parameters which appear in the penalty function is described. Global convergence of the given method is proved.     

A new adaptive trust region algorithm for optimization problems

It is well known that trust region methods are very effective for optimization problems. In this article, a new adaptive trust region method is presented for solving unconstrained optimization problems. The proposed method combines a modified secant equation with the BFGS updated formula and an adaptive trust region radius, where the new trust region radius makes use of not only the function information but also the gradient information. Under suitable conditions, global convergence is proved, and we demonstrate the local superlinear convergence of the proposed method. The numerical results indicate that the proposed method is very efficient.     

求解箱式约束全局优化问题的新的F-C函数（英文）

To solve the global optimization problems which have several local minimizers,a new F-C function is proposes by combining a filled function and a cross function. The properties of the F-C function are discussed and the corresponding algorithm is given in this paper. F-C function has the same local minimizers with the objective function.Therefore, the F-C function method only needs to minimize the objective function once in the first iteration. Numerical experiments are performed and the results show that the proposed method is very effective.     

A new local and global optimization method for mixed integer quadratic programming problems

In this paper, a new local optimization method for mixed integer quadratic programming problems with box constraints is presented by using its necessary global optimality conditions. Then a new global optimization method by combining its sufficient global optimality conditions and an auxiliary function is proposed. Some numerical examples are also presented to show that the proposed optimization methods for mixed integer quadratic programming problems with box constraints are very efficient and stable.     

Global optimality conditions and optimization methods for quadratic integer programming problems

In this paper, we first establish some sufficient and some necessary global optimality conditions for quadratic integer programming problems. Then we present a new local optimization method for quadratic integer programming problems according to its necessary global optimality conditions. A new global optimization method is proposed by combining its sufficient global optimality conditions, local optimization method and an auxiliary function. The numerical examples are also presented to show that the proposed optimization methods for quadratic integer programming problems are very efficient and stable.     

Efficient Mittag-Leffler Collocation Method for Solving Linear and Nonlinear Fractional Differential Equations

In this paper, a new approximation method for fractional differential equations based on Mittag-Leffler function is developed. Finite Mittag-Leffler function and its fractional-order derivatives are investigated. An efficient technique for solving linear and nonlinear fractional order differential equations is developed. The proposed method combines Mittag-Leffler collocation method and optimization technique. Error estimation of the approximation is stated and proved. We present numerical results and comparisons of previous treatments to demonstrate the efficiency and applicability of the proposed method. Making use of small number of unknowns, the resulting solution converges to the exact one in the linear case and it has a very small error in the nonlinear case.     

一种修正的谱CD共轭梯度算法的全局收敛性

In this paper,we present a new nonlinear modified spectral CD conjugate gradient method for solving large scale unconstrained optimization problems.The direction generated by the method is a descent direction for the objective function,and this property depends neither on the line search rule,nor on the convexity of the objective function.Moreover,the modified method reduces to the standard CD method if line search is exact.Under some mild conditions,we prove that the modified method with line search is globally convergent even if the objective function is nonconvex.Preliminary numerical results show that the proposed method is very promising.     

A new kernel function for SPH with applications to free surface flows

Smoothed particle hydrodynamics (SPH) is a popular meshfree Lagrangian particle method, which uses a kernel function for numerical approximations. The kernel function is closely related to the computational accuracy and stability of the SPH method. In this paper, a new kernel function is proposed, which consists of two cosine functions and is referred to as double cosine kernel function. The newly proposed double cosine kernel function is sufficiently smooth, and is associated with an adjustable support domain. It also has smaller second order momentum, and therefore it can have better accuracy in terms of kernel approximation. SPH method with this double cosine kernel function is applied to simulate a dam-break flow and water entry of a horizontal circular cylinder. The obtained SPH results agree very well with the experimental results. The double cosine kernel function is also comparatively studied with two frequently used SPH kernel functions, Gaussian and cubic spline kernel functions.     

非线性耦合Klein-Gordon方程组和耦合Schr\"{o}dinger-Boussinesq方程组的双行波解

本文提出了一种全新复合$(\frac{G''}{G})$展开方法,运用这种新方法并借助符号计算软件构造了非线性耦合Klein-Gordon方程组和耦合Schr\"{o}dinger-Boussinesq方程组的多种双行波解,包括双双曲正切函数解,双正切函数解,双有理函数解以及它们的混合解. 复合$(\frac{G''}{G})$展开方法不但直接有效地求出了两类非线性偏微分方程的双行波解,而且扩大了解的范围.这种新方法对于研究非线性偏微分方程具有广泛的应用意义.