Global Convergence of a Memory Gradient Method for Unconstrained Optimization

Memory gradient methods are used for unconstrained optimization, especially large scale problems. The first idea of memory gradient methods was proposed by Miele and Cantrell (1969) and Cragg and Levy (1969). In this paper, we present a new memory gradient method which generates a descent search direction for the objective function at every iteration. We show that our method converges globally to the solution if the Wolfe conditions are satisfied within the framework of the line search strategy. Our numerical results show that the proposed method is efficient for given standard test problems if we choose a good parameter included in the method.     

一类与BB型对偶剖分相关的广义差分格式

豆引言考虑二阶椭圆方程的边值问题〔,a.an.a.＆t-。^D一[六（a于）十十…于）」一八x,y）,（x,y）En,（1.1）J“山一而“av”-av”。。、一、。。,\一·。·---,l。。、____（.2）LU一0,（J,y）E厂一go,其中D是多边形区域,厂一JD为0的边界,f（x,y）为o上的已知函数/三L‘（0）,系数a—a（xJ）充分光滑,且存在常数7>O,使得以X,y）>/,对任意（X,y）ED.文[1],[2]已系统地研究了求解口.1）,（l.2）的广义差分法.广义差分法的基本思想是对求解区域0作三角形剖分TA及其对偶剖分T;,然后构造T^上的试探函数空间U。（有限元空间）和耳上的…     

带状螺旋线研究中的坐标变换

分析了带状螺旋线行波管中电磁场分量在柱坐标系下的Floquet形式，证明适当的坐标变换是电磁场分量写成变量分离形式的充分条件.螺旋带平面展开后，应用坐标变换得到的电磁场分量变量分离形式是去除面电流分布假设的理论基础.计算并分析了一个典型结构的色散和耦合阻抗，计算结果与实验结果有很好的一致. 关键词： 螺旋带 坐标变换 色散 耦合阻抗     

On interval-valued nonlinear programming problems

The Wolfe's duality theorems in interval-valued optimization problems are derived in this paper. Four kinds of interval-valued optimization problems are formulated. The Karush-Kuhn-Tucker optimality conditions for interval-valued optimization problems are derived for the purpose of proving the strong duality theorems. The concept of having no duality gap in weak and strong sense are also introduced, and the strong duality theorems in weak and strong sense are then derived naturally.     

On the Distance Between Some πps Sampling Designs

Asymptotic distances between probability distributions appearing in πps sampling theory are studied. The distributions are Poisson, Conditional Poisson (CP), Sampford, Pareto, Adjusted CP and Adjusted Pareto sampling. We start with the Kullback-Leibler divergence and the Hellinger distance and derive a simpler distance measure using a Taylor expansion of order two. This measure is evaluated first theoretically and then numerically, using small populations. The numerical examples are also illustrated using a multidimensional scaling technique called principal coordinate analysis (PCO). It turns out that Adjusted CP, Sampford, and adjusted Pareto are quite close to each other. Pareto is a bit further away from these, then comes CP and finally Poisson which is rather far from all the others.      

A note on characteristic classes

This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.     

一个带Hardy项的椭圆方程的多重解

通过对偶变分方法证明了一个带Hardy项和临界非线性的非线性椭圆方程的非平凡解的存在性和多重性.     

Modeling Three-Dimensional Groundwater Flows by the Body-Fitted Coordinate (BFC) Method: II. Free and Moving Boundary Problems

This paper presents a methodology and solution procedure of the time-dependent body-fitted coordinate (BFC) method for the analysis of transient, three-dimensional groundwater flow problems characterized by free and moving boundaries. The technique consists of numerical grid generation, time-dependent body-fitted coordinate transformation, and application of the finite difference method (FDM) to the transformed partial differential equations. Based on the time-dependent BFC method, a three-dimensional finite-difference computer code, BFC3DGW, was developed and used to solve two unconfined flow problems. The code was verified by comparing numerical results with analytical solutions for a steady-state seepage problem. In order to demonstrate capability of the method in dealing with flow problems with irregular and moving boundary surfaces, an unconfined well-flow problem was solved by the developed code. Difficulties associated with the free and moving irregular boundary have been successfully overcome by employing this method.     

Rotation procedure in intrinsic reaction coordinate calculations

A procedure for calculating the distance between two points on an intrinsic reaction coordinate (IRC) obtained from two separate runs is proposed. The procedure mainly involves the rotation of the geometrical configuration of one point in order to obtain a configuration not rotated relative to the other point.     

解整数线性规划中选择割平面的一个方法

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。