ON THE CONVERGENCE OF MULTIPLICATIVE ITERATIVE ALGORITHMS WITH INEXACT LINE SEARCH

1.IntroductionIntillspaperweanalyzetheconvergenceonmultiplicativeiterativealgorithmsfortheIninimizationofadiffcrentiablefunctiondefinedonthepositiveorthantofR".ThealgorithmissllggestedbyEggermolltl'],andisrelatedtotheEM[2](Expextation--Maximization)algoritllnlforPositronemissiontonlography[']andimagereconstructi..14].Wecollsidertheproblenl"linf(x)s.t.x20.Themultiplicativeiterativealgorithmshavethel'orlniforj=l,2,',n,withAhdeterminedthroughalinesearch.Whilelusem[5]establishedanelegantconv…     

大学物理课程网络辅助教学系统的构建与应用

本文介绍了上海交通大学大学物理课程网络辅助教学系统的设计思想、整体结构和主要的功能模块，概述了运用网络辅助教学系统实施“课堂教学＋网络辅助教学”：这种教学模式的应用情况．     

一种基于GIS的选址问题及算法

本文考虑了选址区域内存在地理阻断情况下的一种基于GIS的选址问题.对单配送中心选址模型,以GIS返回的任意两点间的最短可行路径的长度作为修正距离函数,分析了目标函数在凸形选址区域上非凸非连续的性质.进一步,采用给出了一种近似搜索算法并通过一个实例计算与重心法进行了比较.     

A search technique for global optimization in a chaotic environment

We describe a new algorithm which uses the trajectories of a discrete dynamical system to sample the domain of an unconstrained objective function in search of global minima. The algorithm is unusually adept at avoiding nonoptimal local minima and successfully converging to a global minimum. Trajectories generated by the algorithm for objective functions with many local minima exhibit chaotic behavior, in the sense that they are extremely sensitive to changes in initial conditions and system parameters. In this context, chaos seems to have a beneficial effect: failure to converge to a global minimum from a given initial point can often be rectified by making arbitrarily small changes in the system parameters.     

不连续不可逆二维映象的动力学特性

总结两个保守映象不可逆地分段连续链接(称为类耗散系统)以及一个保守映象与一个耗散映象不可逆地分段连续链接(称为半耗散系统)情况下得到的五项共同动力学特征：不连续边界象集构成的随机网成为唯一的混沌轨道；由于某些相点具有两个逆象而导致的相空间塌缩(类耗散)；由于系统的不连续不可逆性质而出现的胖分形禁区网；在具有吸引子共存时占据不连续边界象集随机网和胖分形禁区网区域的点滴状吸引域以及由此导致的吸引子不可预言性；即使在传统强耗散存在的情况下点滴状吸引域仍由类耗散机制主宰.以一个累积-触发电路为例，说明这五项系统动 关键词： 随机网 禁区网 点滴状吸引域     

一个线性约束优化问题的广义梯度投影法

本文对线性约束优化问题提出了一个新的广义梯度投影法，该算法采用了非精确线性搜索，并在每次迭代运算中结合了广义投影矩阵和变尺度方法的思想确定其搜索方向．在通常的假设条件下，证明了该算法的整体收敛性和超线性收敛速度．     

一种改进的进化规划算法

本对于全局优化问题提出一个改进的进化规划算法，该算法以概率p接收基于电磁理论求出合力方向作为随机搜索方向，以概率1-p接收按正态分布产生的随机搜索方向。改进算法不仅克服了传统进化规划算法随机搜索的盲目性，而且保留了传统进化规划算法全局搜索性。本算法应用于几个典型例题，数值结果表明本算法是可行的，有效的。     

二维椭圆型方程反问题中优化算法的比较

近年来，决定椭圆型方程系数反问题在地磁、地球物理、冶金和生物等实际问题上有着广泛的应用．本文讨论了二维的决定椭圆型方程系数反问题的数值求解方法．由误差平方和最小原则，这个反问题可化为一个变分问题，并进一步离散化为一个最优化问题，其目标函数依赖于要决定的方程系数．本文着重考察非线性共轭梯度法在此最优化问题数值计算中的表现，并与拟牛顿法作为对比．为了提高算法的效率我们适当选择加快收敛速度的预处理矩阵．同时还考察了线搜索方法的不同对优化算法的影响．数值实验的结果表明，非线性共轭梯度法在这类大规模优化问题中相对于拟牛顿法更有效．     

Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems

The spectral projected gradient method SPG is an algorithm for large-scale bound-constrained optimization introduced recently by Birgin, Martínez, and Raydan. It is based on the Raydan unconstrained generalization of the Barzilai-Borwein method for quadratics. The SPG algorithm turned out to be surprisingly effective for solving many large-scale minimization problems with box constraints. Therefore, it is natural to test its perfomance for solving the sub-problems that appear in nonlinear programming methods based on augmented Lagrangians. In this work, augmented Lagrangian methods which use SPG as the underlying convex-constraint solver are introduced (ALSPG) and the methods are tested in two sets of problems. First, a meaningful subset of large-scale nonlinearly constrained problems of the CUTE collection is solved and compared with the perfomance of LANCELOT. Second, a family of location problems in the minimax formulation is solved against the package FFSQP.