一项从CAA到CAD的工作～正交优化法SPICE相结合

电子电路的计算机辅助设计方法是促进电子技术发展的一种有效工具。本文介绍如何将行有效的正交优化法与国际盛行的模拟电子电路的分析程序ＳＰＩＣＥ相结合，形成了ＡＣＯＤ软件，将ＣＡＡ扩展为ＣＡＤ。     

“正交法与三次设计”DVD光盘投入使用

产品质量差、经济效益低是企业中普遍存在的老问题。“正交法”是解决这个问题的有效的现代化管理方法之一。它是一种试验设计和最优化方法，是一种投入很低、产出很高的通用技术。“正交法”对于工艺改革、技术革新、产品设计、科学实验和经济计划等影响巨大。     

一维参数化正交小波滤波器的解析性质与优化逼近

本文给出了一维参数化正交小波滤波器系数向量的解析表达式和它的递推计算公式,还给出了它的一阶变分及二阶变分公式．利用这些结果和最优化方法,给出了FIR正交小波滤波器的逼近和设计问题的优化模型和数值例子．     

用正交试验法优化耐磨钢的成分和工艺

本文对影响奥氏体锰钢组织和性能的多种因素，采用正交试验方差分析法，寻求化学成分和热处理工艺的最优设计，生产验证试验表明：按正交试验优化结果制成的风扇磨冲击板，其金属消耗量较低，使用寿命比原用高锰钢有较大提高，达到国内先进水平．     

RAS法迭代误差的正交设计

本文应用正交试验设计手段，对编制投入产出表常用的方法──ＲＡＳ法，就有关传递误差进行了计算，这在国内外尚属首次。计算结果表明，ＲＡＳ的这代误差不可忽视，这一研究具有重要理论价值和实践意义。     

求解简单界约束优化问题的一种逐次逼近法

１引言考虑变量带简单界约束的非线性规划问题：其中二阶连续可微,ａ＝（ａ１,ａ２,…,ａｎ）,ｂ＝（ｂ１,ｂ２,…,ｂｎ）,＋ｉ＝１,２,…,ｎ．问题（１）不仅是实际应用中出现的简单界约束最优化问题,而且相当一部分最优化问题可以把变量限制在有意义的区间内（参见［１］）．因此无论在理论方面还是在实际应用方面,都有研究此类问题并给出简便而有效算法的必要．假设ｆ是凸函数,记ｇ（ｘ）＝ｆ（ｘ）,则由Ｋ－Ｔ条件,问题（１）可化为求解下面的非光滑方程组：显然,（２）等价于易证,（３）等价于求解下面的非光滑方程…     

正交约束优化问题的一阶算法

带有正交约束的矩阵优化问题在材料计算、统计及数据分析等领域中有着广泛的应用.由于正交约束的可行域是Stiefel流形,一直以来流形上的优化方法是求解这一问题的主要方法.近年来,随着实际应用问题所要求的变量规模的扩大,传统的流形优化方法在计算上的劣势显现出来,而一些迭代简单、收敛快的新算法逐渐被提出.通过收缩方法、非收缩可行方法、不可行方法三个类别分别来介绍求解带有正交约束的矩阵优化问题的最新算法.通过分析这些方法的主要特性,以及应用问题的要求,对这类问题算法设计的研究进行了展望.     

泛函梯度数值计算的一种新方法—正交试验法

本文研究并揭示了L_(2~a)(2~(2~a-1))型正交表行(列)间的递推规律,提出了一种泛函梯度数值计算的新方法——正交试验法,该方法在计算速度和精度上优于直接梯度法;在通用性及节省内存方面优于伴随算子法。     

实数域上从正交群到一般线性群的同态

设ｎ,ｍ是自然数且ｎ≥ｍ,本文确定了实数域上从ｎ阶正交群到ｍ阶一般线性群的同态形式．     

从球面到紧致光滑流形的连续映射

本文研究了球面到紧致光滑流形的连续映射的性质.利用Brouwer映射度理论和微分拓扑的基本方法,得到了Munkholm型定理.     

A new approach with orthogonal array for global optimization in design of experiments

In this paper, we develop an approach that determines the overall best parameter setting in design of experiments. The approach starts with successive orthogonal array experiments and ends with a full factorial experiment. The setup for the next orthogonal-array experiment is obtained from the previous one by either fixing a factor at a given level or by reducing the number of levels considered for all currently non-fixed factors. We illustrate this method using an industrial problem with seven parameters, each with three levels. In previous work, the full factorial of 3⁷ = 2,187 points was evaluated and the best point was found. With the new method, we found the same point using 3% of these evaluations. As a further comparison, we obtained the optimum using a traditional Taguchi approach, and found it corresponded to the 366th of the 2,187 possibilities when sorted by the objective function. We conclude the proposed approach would provide an accurate, fast, and economic tool for optimization using design of experiments.     

Kriging metamodeling in simulation: A review

This article reviews Kriging (also called spatial correlation modeling). It presents the basic Kriging assumptions and formulas—contrasting Kriging and classic linear regression metamodels. Furthermore, it extends Kriging to random simulation, and discusses bootstrapping to estimate the variance of the Kriging predictor. Besides classic one-shot statistical designs such as Latin Hypercube Sampling, it reviews sequentialized and customized designs for sensitivity analysis and optimization. It ends with topics for future research.     

经济最优化意义下消耗系数的调整

本文基于“正特片矢量法”,提出了一种在经济最优化意义下调整消耗系数的方法.该方法能够综合考虑产综和价格对消耗系数的影响,有着较好的普适性,在计算上简便易行、效果良好,且具有明显的经济意义.     

W(2)到Kac模的权导子空间

本文研究了 Witt型模李超代数W(2)到Kac模K(λ)的权导子空间问题.利用分类讨论及线性方程组求解的方法,获得了W(2)到K(A)的权导子空间要么是零维要么是一维的结果,推广了李代数到其模的权导子空间的相应结果.     

Shaping an antenna radiation diagram with discrete weights using the PSO algorithm and periodic and nest spaces

Using traditional methods, finding the weights that allow shaping a desired radiation diagram for an antenna in order to reject unwanted signals or maximize the desired signal reception, is possible.However, neither by iterative nor closed methods, can it be done while restricting the amplitudes and phases to a set of finite values for each of them. Also, it often happens that they cannot include in its formulation other types of specifications that are necessary to be achieved.Some modifications were implemented in the method Particle Swarm Optimization (PSO), which reduced the convergence time, especially in the search space of phases where there exists a periodicity that the original method does not take into account.PSO is an evolutionary algorithm, inspired by the social behavior of flocks of birds or fish, developed by Eberhart and Kennedy in 1995, and has been intensively applied in solving numerical Engineering problems.     

Design and operation issues using NLP superstructure modeling

Till present, models that determined batch plants configurations in the chemical process industry resorted to models with binary variables to represent the different admissible options. This approach allowed representing the problem in a simple way while considering a significant number of alternatives. Nevertheless, the non-convexity that arises when dealing with detailed models for representing the involved units operation prevents its correct resolution or has a low performance. This work presents a representation of the problem through a superstructure that takes explicitly into account all the alternatives without resorting to binary variables. By using extremely simple modeling, it is possible to manage an appropriate number of options for this type of problems by means of a non-linear programming (NLP) model. Moreover, it is possible to consider duplication in series of production stages, which is an alternative that has not been used till now. This approach is posed for the case of a fermentors network. The solution is reached with very low requirements as regards employed computer time and without the aforementioned difficulties.     

Acceleration of the leastpth algorithm for minimax optimization with engineering applications

Over the past few years a number of researchers in mathematical programming and engineering became very interested in both the theoretical and practical applications of minimax optimization. The purpose of the present paper is to present a new method of solving the minimax optimization problem and at the same time to apply it to nonlinear programming and to three practical engineering problems. The original problem is defined as a modified leastpth objective function which under certain conditions has the same optimum as the original problem. The advantages of the present approach over the Bandler-Charalambous leastpth approach are similar to the advantages of the augmented Lagrangians approach for nonlinear programming over the standard penalty methods.This work was supported by the National Research Council of Canada under Grant A4414, and from the University of Waterloo.     

A Constraint Satisfaction Approach to a Circuit Design Problem

A classical circuit-design problem from Ebers and Moll (1954) features a system of nine nonlinear equations in nine variables that is very challenging both for local and global methods. This system was solved globally using an interval method by Ratschek and Rokne (1993) in the box [0, 10]⁹. Their algorithm had enormous costs (i.e., over 14 months using a network of 30 Sun Sparc-1 workstations) but they state that ‘at this time, we know no other method which has been applied to this circuit design problem and which has led to the same guaranteed result of locating exactly one solution in this huge domain, completed with a reliable error estimate’. The present paper gives a novel branch-and-prune algorithm that obtains a unique safe box for the above system within reasonable computation times. The algorithm combines traditional interval techniques with an adaptation of discrete constraint-satisfaction techniques to continuous problems. Of particular interest is the simplicity of the approach. This revised version was published online in July 2006 with corrections to the Cover Date.     

从矩阵迹关系过渡到算子迹关系的一个通用方法

本文给出了一个将矩阵迹的不等式推广为Ｈｉｌｂｅｒｔ空间中算子迹的不等式的方法，并用它较简捷地将矩阵论中Ｂｅｌｌｍａｎ问题的已有结果以及其它一些矩阵迹的不等式推广为算子迹的相应不等式。