Adaptive Algorithm for Constrained Least-Squares Problems

This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.     

具有模糊数的模糊多目标群体决策优选模型与方法

多目标群体决策问题是运筹学的一个重要研究领域，目前已经提出了一些有效的决策方法。但对目标值和权重均为模糊数的模糊多目标群体决策问题却研究不多，本对此类模糊多目标群体决策问题进行了探讨，利用相对正理想方案与相对负理想方案概念定义了相对差异距离，进而建立了模糊多目标群体决策优选模型与方法，并通过战役决心方案的评价说明了该方法是可行、有效的，可作为军事决策与决策支持系统的备选方法。     

Patterns and Symmetries in the Visual Cortex and in Natural Images

As borders between different entities, lines are an important element of natural images. Indeed, the neurons of the mammalian visual cortex are tuned to respond best to lines of a given orientation. This preferred orientation varies continuously across most of the cortex, but also has vortex-like singularities known as pinwheels. In attempting to describe such patterns of orientation preference, we are led to consider underlying rotation symmetries: Oriented segments in natural images tend to be collinear; neurons are more likely to be connected if their preferred orientations are aligned to their topographic separation. These are indications of a reduced symmetry requiring joint rotations of both orientation preference and the underlying topography. This is verified by direct statistical tests in both natural images and in cortical maps. Using the statistics of natural scenes we construct filters that are best suited to extracting information from such images, and find qualitative similarities to mammalian vision. PACS84.35+i 89.70.+c 87.57.Nk     

Global and uniform convergence of subspace correction methods for some convex optimization problems

This paper gives some global and uniform convergence estimates for a class of subspace correction (based on space decomposition) iterative methods applied to some unconstrained convex optimization problems. Some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems.

     

Calibrating software reliability models when the test environment does not match the user environment

Software failures have become the major factor that brings the system down or causes a degradation in the quality of service. For many applications, estimating the software failure rate from a user's perspective helps the development team evaluate the reliability of the software and determine the release time properly. Traditionally, software reliability growth models are applied to system test data with the hope of estimating the software failure rate in the field. Given the aggressive nature by which the software is exercised during system test, as well as unavoidable differences between the test environment and the field environment, the resulting estimate of the failure rate will not typically reflect the user‐perceived failure rate in the field. The goal of this work is to quantify the mismatch between the system test environment and the field environment. A calibration factor is proposed to map the failure rate estimated from the system test data to the failure rate that will be observed in the field. Non‐homogeneous Poisson process models are utilized to estimate the software failure rate in both the system test phase and the field. For projects that have only system test data, use of the calibration factor provides an estimate of the field failure rate that would otherwise be unavailable. For projects that have both system test data and previous field data, the calibration factor can be explicitly evaluated and used to estimate the field failure rate of future releases as their system test data becomes available. Copyright © 2002 John Wiley & Sons, Ltd.     

ON HYPERBOLIC TIME DISCOUNTING IN EXHAUSTIBLE RESOURCE MODELS: AN APPLICATION TO WORLD OIL RESOURCES

ABSTRACT. Recent research on discounting in long term economic models involves hyperbolic discounting, in which the marginal discount rate shrinks as time passes. To investigate hyperbolic discounting and exhaustible resource allocation, this work develops a discrete‐time world oil model and model solution procedure, then uses the model to examine the consequences of adopting conventional (constant annual) discounting when hyperbolic discounting is appropriate, of adopting one hyperbolic discount rate path when a different hyperbolic path is appropriate, and of adopting hyperbolic discounting when conventional discounting is appropriate. Five conventional and two hyperbolic discount rate paths are considered. One hyperbolic path is that used by Nordhaus and Boyer [2000]; the other is that recommended by Weitzman [2001]. The generality of the findings is also assessed.     

叶型优化在非定常流动条件下效果的数值分析

本文对叶型优化在非定常流动条件下的效果进行数值研究。叶型优化基于比较成熟的在定常流动条件下的反问题解法，非定常流动则考虑到动静叶栅之间的相互作用，非定常流动的求解在Ｎ－Ｓ方程的基础上采用分区计算的方法来完成。数值计算的结果表明，定常流动条件下优化得到的叶型在非定常流动条件下同样具有较好的气动性能。     

基于自适应预测滤波理论的模数转换器设计方法

基于自适应差分量化理论，提出了在不增加转换位数的情况下提高模数转换器(ADC)动态范围的一种设计方法。该方法通过量化输入与预测的差值来获得预测增益，从而扩大ADC的动态范围；通过差分量化值与预测值相加得到输出信号，并将该分别采用LMS和RLS算法进行处理．得到输入信号的预测值．计算机模拟结果证实，上述两种算法均能使模数转换器的动态范围提高约25dB．比较而言，RLS算法收敛速度更快，收敛性更好，但计算量较大．     

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．     

对求解非线性方程方法的探索

BaiCL在2001年提出了双曲函数法，并把解设成具体的双曲函数，即sinhw和coshw的线性组合．本文把解设成是由2个函数f(ξ)和g(ξ)组成的线性组合，它们可以有多种取法，从而使方程更直接、更有效．借助数学软件Maple，用改进后的方法和吴文俊消元法，求解Bai C L文中的一个例子，获得了包含Bai文结果在内的更为丰富、精确的行波解．