Convergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition

In this paper, we present the new trust region method for nonlinear equations with the trust region converging to zero. The new method preserves the global convergence of the traditional trust region methods in which the trust region radius will be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition which is weaker than the nonsingularity. An example given by Y.X. Yuan shows that the convergence rate can not be quadratic. Finally, some numerical results are given. This work is supported by Chinese NSFC grants 10401023 and 10371076, Research Grants for Young Teachers of Shanghai Jiao Tong University, and E-Institute of Computational Sciences of Shanghai Universities. An erratum to this article is available at .     

Computing Aviation Sparing Policies: Solving a Large Nonlinear Integer Program

Deployed US Navy aircraft carriers must stock a large number of spare parts to support the various types of aircraft embarked on the ship. The sparing policy determines the spares that will be stocked on the ship to keep the embarked aircraft ready to fly. Given a fleet of ten or more aircraft carriers and a cost of approximately 50 million dollars per carrier plus the cost of spares maintained in warehouses in the United States, the sparing problem constitutes a significant portion of the Navy’s resources. The objective of this work is to find a minimum-cost sparing policy that meets the readiness requirements of the embarked aircraft. This is a very large, nonlinear, integer optimization problem. The cost function is piecewise linear and convex while the constraint mapping is highly nonlinear. The distinguishing characteristics of this problem from an optimization viewpoint are that a large number of decision variables are required to be integer and that the nonlinear constraint functions are essentially “black box” functions; that is, they are very difficult (and expensive) to evaluate and their derivatives are not available. Moreover, they are not convex. Integer programming problems with a large number of variables are difficult to solve in general and most successful approaches to solving nonlinear integer problems have involved linear approximation and relaxation techniques that, because of the complexity of the constraint functions, are inappropriate for attacking this problem. We instead employ a pattern search method to each iteration of an interior point-type algorithm to solve the relaxed version of the problem. From the solution found by the pattern search on each interior point iteration, we begin another pattern search on the integer lattice to find a good integer solution. The best integer solution found across all interations is returned as the optimal solution. The pattern searches are distributed across a local area network of non-dedicated, heterogeneous computers in an office environment, thus, drastically reducing the time required to find the solution.     

Successive column correction algorithms for solving sparse nonlinear systems of equations

This paper presents two algorithms for solving sparse nonlinear systems of equations: the CM-successive column correction algorithm and a modified CM-successive column correction algorithm. Aq-superlinear convergence theorem and anr-convergence order estimate are given for both algorithms. Some numerical results and the detailed comparisons with some previously established algorithms show that the new algorithms have some promise of being very effective in practice.This research was partially supported by contracts and grants: DOE DE-AS05-82ER1-13016, AFOSR 85-0243 at Rice University, Houston, U.S.A. and Natural Sciences and Engineering Research Council of Canada grant A-8639.     

利用驻波实验研究混沌现象

利用驻波实验演示了混沌现象,并对其进行了理论分析和计算机仿真研究.仿真结果与实验结果都表明:当连接点接近驻波波节处时,振动系统处于混沌运动状态;而当连接点接近驻波波腹处时,系统处于稳定驻波运动状态.     

核磁共振成像一维空间编码教学实验

利用梯度磁场实现检测信号的空间编码,是核磁共振成像(MRI)的关键技术.本文采用ccc系列样品将二维问题简化为一维,使用超小型教学用核磁共振成像仪进行了一维空间编码实验研究,并对实验过程及实验结果进行了计算模拟和分析.     

0.86μm激光扫描二维成像的实验研究

本文给出作者设计的0.86μm激光二维成像系统的原理框图、成像雷达距离方程和部分物体对0.86μm激光的反射对比度的测试数据,并展示了各类物体激光成像的照片.     

一类非线性常微分方程振荡解的渐近表示

在本文中,我们讨论了非线性常微分方程y"=a0|x|αy3 a1|x|βy2 α2|x|γy α3|x|δ振荡解的渐近表示．在这个方程中将α0,α,α1,β,α2,γ,α3,δ分别换成0,0,6,0,0,0,sgn(x),1就是著名的第一类Painleve方程,而将α0,α,α1,β,α2,γ,α3,δ分别换成2,0,0,0,sgn(x),1,α0,就是著名的第二类Painleve方程．当α0,α,α1,β,α2,γ,α3,δ分别换成-β/3γ,0,0,0,1/γ,1,α,0时,可用于组合KdV方程孤立子解的化简．     

用离子速度影象技术研究n-C4H9Br的光解

利用离子速度影象技术研究了正一溴丁烷(n-C4H9Br)在231~267 nm波段的光解,得出了如下结论:正一溴丁烷(n-C4H9Br)在231~267 nm波段的吸收源于基态到三个最低激发态的跃迁,这三个激发态标识为1A″、2A′和3A′;发生在这三个排斥态的势能面(PES)上的光解最终导致C4H9 Br(2P3/2)或C4H9 Br*(2P1/2)的产生;2A′和3A′态之间存在避免交叉(Avoided crossing)会影响最终的光解产物;从基态1A′到激发态1A″的跃迁矩垂直于对称面,也就垂直于C-Br键;从基态1A′到激发态3A′的跃迁矩平行于对称面,同时平行于C-Br键;从基态1A′到激发态2A′的跃迁矩在对称面内,且与C-Br键成53.1°夹角.我们也讨论了正一溴丁烷(n-C4H9Br)在234 nm和267 nm附近光解时的避免交叉几率(Avoided crossingprobability),以及它对单通道相对产额(Relative fraction of the individual pathways)的影响.     

红外动态图像生成技术概念研究

红外动态图像生成技术的基本概念包括基本术语及其定义。为了描述红外动态图像生成技术的特性,通常采用如光源类型、光谱波段、阵列规模、空间分辨率、填充因子、时间常数、帧频、闪烁、温度范围、串扰、均匀性、发射率、辐射对比度、动态范围、温度分辨率、调制传递函数、几何畸变及最大温度和最大辐射强度等概念。介绍了描述红外动态图像生成系统性能的基本概念的定义。转换器的指标定义对于转换器的设计和性能指标的测试都有重要的意义。     

一类Marangoni对流边界层方程的近似解析解

利用Adomain解析拆分和Padé逼近方法对由Marangoni对流诱发的层流边界层问题进行了研究, 提供了一种求解边界层方程的解析分析方法. 得到了问题的近似解析解并对相应的流动及传热特性进行了探讨. 本文所提出的思想方法可以用于解决其他科学和工程技术问题. 关键词： Marangoni对流 非线性 Adomain拆分法 近似解析解