关于“评测指标权重确定的结构熵权法”的注记

本文基于文献[1]所提出的观点,根据熵理论和德尔斐专家调查法,对文献[1]所提出的方法进行了改进,得到了改进的结构熵权法,并运用此方法对环保项目指标进行权重确定,同时与经典的德尔斐专家调查法确定的权重进行比较,并对二者的差异作出了合理解释。     

参数设计中的方差估计

本文根据参数设计的特点,从条件分布的角度提出了参数设计中方差估计的方法,并对可计算性项目给出了相应的方差估计方式。对一个可计算性项目分别用田口的“直积法”和本文所提出的方法进行了分析,并与随机模拟的结果作了比较,结果表明本文所提出的方法与随机模拟的结果非常接近,而“直积法”与其相距较远。     

隐式极限状态方程可靠性研究

针对非线性隐式极限状态方程失效概率的计算,提出了精度更高的改进的均值二次法,并提出了与响应面法相结合的改进均值法,给出了所提方法的实现策略.具体算例表明,改进的均值二次法的精度较改进的均值一次法有明显提高,而改进均值法与响应面法结合后的精度改善更为明显,并且这种结合方法对响应面法的插值点位置不敏感,插值点在较大范围内变化均能得到稳健的高精度结果,从而说明所提方法的有效性.     

具有充分下降性的改进FR共轭梯度法

本文研究了大规模无约束优化问题,提出了一个基于改进的FR共轭参数公式的共轭梯度法.不依赖于任何线搜索准则,算法所产生的搜索方向总是充分下降的.在标准Wolfe线搜索准则下,获得了新算法的全局收敛性.最后,对所提出的算法进行了初步数值实验,其结果表明所改进的方法是有效的.     

关于扩散方程漂移系数估计方法的改进

本文提出了一种新的基于扩散过程轨道构造漂移系数样本的方法—对数增量法,通过理论及模拟分析说明了在适当条件下,特别是对于大多数金融数据,基于对数增量法获得的漂移系数估计量的收敛速度及有限样本性质均比基于传统的"直接增量法"所得到的结果要好。     

一个自调节Polak-Ribiere-Polyak型共轭梯度法

共轭梯度法是求解大规模无约束优化问题最有效的方法之一.基于Polak-RibièrePolyak(PRP)共轭梯度法具有较弱的收敛性和较好的数值表现,而Fletcher-Reeves(FR)共轭梯度法则反之,本文研究PRP共轭梯度法的一个自调节改进.在PRP公式引入调节因子,并据此提出了一个自调节PRP共轭梯度法.改进的方法具有PRP方法所特有的性质(*)及FR方法良好的收敛性·在强Wolfe非精确线搜索条件和常规假设下,证明了新方法不仅满足充分下降条件,而且全局收敛.最后,对新算法进行数值测试并与其他同类方法进行比较,结果表明所提方法是有效的.     

用向量直接求二面角C-AB-D

现行求二面角,通用"平面的法向量法",即通过二面角的两个半平面的法向量所成的角间接地去求.由于半平面的法向量的方向本身不确定,所以求出的角不一定是需求的二面角.这里提出一种用向量直接求二面角的方法,供读者参考.     

建立在割线条件上的新Liu-Storey型共轭梯度法的全局收敛性(英文)

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.     

岭回归中基于广义交叉核实法的最优模型平均估计

岭回归是一种常用的用于克服多重共线性的压缩估计方法.文章在存在异方差的背景下,考察了组合不同岭参数下岭估计量的模型平均方法,并在广义交叉核实法的框架下构造了相应的权重选择准则.当拟合模型的设定存在偏误时,证明了基于广义交叉核实法的模型平均法可以给出渐近最优的预测.此外,使用蒙特卡洛模拟考察了所提出的模型平均方法在有限样本下的有效性.最终,使用所提出的方法对一组乙炔反应工艺的数据进行了分析,所得到的结论进一步表明,模型平均法在实际数据分析工作中具有较高应用价值.     

对TOPSIS法用于综合评价的改进

本文指出了 TOPSIS法用于综合评价所存在的问题 ,并提出了相应的改进方法 ,使 TOPSIS法用于综合评价以及多目标决策分析更趋完善 ,所得分析评价结果更合理更客观     

求解加权线性最小二乘问题的一类预处理GAOR方法

为了快速求解一类来自加权线性最小二乘问题的2×2块线性系统,本文提出一类新的预处理子用以加速GAOR方法,也就是新的预处理GAOR方法.得到了一些比较结果,这些结果表明当GAOR方法收敛时,新方法比原GAOR方法和之前的一些预处理GAOR方法有更好的收敛性.而且,数值算例也验证了新预处理子的有效性．     

一个四阶收敛的牛顿类方法

A fourth-order convergence method of solving roots for nonlinear equation,which is a variant of Newton's method given.Its convergence properties is proved.It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end,numerical tests are given and compared with other known Newton and Newtontype methods.The results show that the proposed method has some more advantages than others.It enriches the methods to find the roots of non-linear equations and it ...     

A class of conjugate gradient methods for convex constrained monotone equations

The recent designed non-linear conjugate gradient method of Dai and Kou [SIAM J Optim. 2013;23:296–320] is very efficient currently in solving large-scale unconstrained minimization problems due to its simpler iterative form, lower storage requirement and its closeness to the scaled memoryless BFGS method. Just because of these attractive properties, this method was extended successfully to solve higher dimensional symmetric non-linear equations in recent years. Nevertheless, its numerical performance in solving convex constrained monotone equations has never been explored. In this paper, combining with the projection method of Solodov and Svaiter, we develop a family of non-linear conjugate gradient methods for convex constrained monotone equations. The proposed methods do not require the Jacobian information of equations, and even they do not store any matrix in each iteration. They are potential to solve non-smooth problems with higher dimensions. We prove the global convergence of the class of the proposed methods and establish its R-linear convergence rate under some reasonable conditions. Finally, we also do some numerical experiments to show that the proposed methods are efficient and promising.     

一类修正的Halley迭代法的统一收敛性定理

In this paper a class of modified Halley iteration methods for simultaneously finding polynomial zeros is discussed. A unified convergence theorem is proposed and the efficiency analysis is given.     

连续化方法求解变分不等式问题

利用变分不等式问题的KKT条件,给出了连续化方法求解变分不等式问题的一般框架,该框架包含了现存的几种连续方法;并给出一种求解的基本算法,证明了基本算法的可行性及算法的收敛性;最后用数值试验验证了算法的稳定性和有效性。     

A Class of Projection Methods for General Variational Inequalities

In this paper, we consider and analyze a new class of projection methods for solving pseudomonotone general variational inequalities using the Wiener-Hopf equations technique. The modified methods converge for pseudomonotone operators. Our proof of convergence is very simple as compared with other methods. The proposed methods include several known methods as special cases.     

A Steffensen-like method and its higher-order variants

For solving nonlinear equations, we suggest a second-order parametric Steffensen-like method, which is derivative free and only uses two evaluations of the function in one step. We also suggest a variant of the Steffensen-like method which is still derivative free and uses four evaluations of the function to achieve cubic convergence. Moreover, a fast Steffensen-like method with super quadratic convergence and a fast variant of the Steffensen-like method with super cubic convergence are proposed by using a parameter estimation. The error equations and asymptotic convergence constants are obtained for the discussed methods. The numerical results and the basins of attraction support the proposed methods.     

A Newton linearized compact finite difference scheme for one class of Sobolev equations

In this article, a Newton linearized compact finite difference scheme is proposed to numerically solve a class of Sobolev equations. The unique solvability, convergence, and stability of the proposed scheme are proved. It is shown that the proposed method is of order 2 in temporal direction and order 4 in spatial direction. Moreover, compare to the classical extrapolated Crank‐Nicolson method or the second‐order multistep implicit–explicit methods, the proposed scheme is easier to be implemented as it only requires one starting value. Finally, numerical experiments on one and two‐dimensional problems are presented to illustrate our theoretical results.     

A preconditioned and extrapolation-accelerated GMRES method for PageRank

In this paper, we propose and analyze GMRES-type methods for the PageRank computation. However, GMRES may converge very slowly or sometimes even diverge or break down when the damping factor is close to 1 and the dimension of the search subspace is low. We propose two strategies: preconditioning and vector extrapolation accelerating, to improve the convergence rate of the GMRES method. Theoretical analysis demonstrate the efficiency of the proposed strategies and numerical experiments show that the performance of the proposed methods is very much better than that of the traditional methods for PageRank problems.     

A globally convergent BFGS method for nonlinear monotone equations without any merit functions

Since 1965, there has been significant progress in the theoretical study on quasi-Newton methods for solving nonlinear equations, especially in the local convergence analysis. However, the study on global convergence of quasi-Newton methods is relatively fewer, especially for the BFGS method. To ensure global convergence, some merit function such as the squared norm merit function is typically used. In this paper, we propose an algorithm for solving nonlinear monotone equations, which combines the BFGS method and the hyperplane projection method. We also prove that the proposed BFGS method converges globally if the equation is monotone and Lipschitz continuous without differentiability requirement on the equation, which makes it possible to solve some nonsmooth equations. An attractive property of the proposed method is that its global convergence is independent of any merit function.We also report some numerical results to show efficiency of the proposed method.