线性规划初始基可行解的一种直接算法

本文通过引入可变动目标函数的预规划来求线性的初始基可行解，可以大量减少外额变量的个数，从而简化了二阶段单纯形法，使之便于在计算机上实现。     

对单纯形算法的两点改进意见

本文指出两点:1.按照最速下降规则确定进基和离基变量,既能避免迭代循环,又常减少迭代次数;2.可不直接引入人工变量求初始基可行解,并从一开始就考虑按一定意义下使原目标函数下降最多的原则选择基变量,使得到的初始基可行解尽可能的好。 1.关于最速下降规则设所论线性规划问题由表1给出: 最速下降规则可叙述如下: (A)设R={j|λ_j>0},对每一j∈R,计算     

单纯形法的旋转迭代算法及影子价格

本文对线性规划问题提出一种寻找初始可行基和判定可行解的统一方法，它在运用单纯形法时，在若干情况下不必引入人工变量而可在一种表格之下直接应用旋转运算而获得，之后就在同一张表格下完全和常规单纯形法一样求最优解，此法我们称之为“单纯形法的旋转迭代算法”，应用此法，我们容易求出影子价格。     

初始可行基的判定

用高等数学的理论和方法,对无初始可行基的线性规划问题解的存在性及求解方法进行研究,得出关于无初始可行基的线性规划问题解的存在性的六个定理,回答了无初始可行基的线性规划问题解的存在条件和该问题的初始可行基的确定方法.     

关于<用初等行变换解一类线性规划问题>一文的注记

本指出，在献[1]提出的求解线性规划的方法中，对于初始可行基、最优解和零解的存在性问题所得出的某些结论是错误的，特殊是如果含n个变量的约束条件的增广矩阵经初等行变换后，其中某行的前n个分量非正，而最后一个分量为0时，应认为该线性规划问题可能有非零解，且不一定存在零解，而非[1]所述的结论。     

直接求线性规划可行基的一种方法

本文给出直接求线性规划问题基可行解的一种简易方法,该方法既避免了引入人工变量,减少存储,一般又能较快地得到一个较好的基可行解.     

线性规划问题的多项式算法

<正> 大家知道,用电子计算机解一个数学问题时,一个算法的好坏通常是用它的计算量、存储量等指标来衡量。在算法分析中,若以 L 表示某一数学问题的规模(例如变量的个数、方程的个数、初始数据写成二进制数码的长度等等),一个算法,如果它所需要的基本运算(如+、-、×、÷,比较等)的次数是 L 的多项式函数,我们就称这个算法是多项式算法.多     

一种原始——对偶单纯形算法的枢轴准则选择

Curet曾提出了一种有趣的原始一对偶技术,在优化对偶问题的同时单调减少原始不可行约束的数量,当原始可行性产生时也就产生了原问题的最优解.然而该算法需要一个初始对偶可行解来启动,目标行的选择也是灵活、不确定的.根据Curet的原始一对偶算法原理,提出了两种目标行选择准则,并通过数值试验进行比较和选择.对不存在初始对偶可行解的情形,通过适当改变目标函数的系数来构造一个对偶可行解,以求得一个原始可行解,再应用原始单纯形算法求得原问题的最优解.数值试验对这种算法的计算性能进行验证,通过与经典两阶段单纯形算法比较,结果表明,提出的算法在大部分问题上具有更高的计算效率.     

线性规划的支撑方法（二）

线性规划的支撑方法（二）高学东，武森，李宗元（北京科技大学管理学院，北京１０００８３）６初始支撑可行解的构造６．１初始可行解的构造在研制或设计一种新产品的时候，初始设计往往可以用来帮助构造数学模型，相应的设计向量天虽不一定完全可行，但在某些方面有可能...     

求解线性不等式组的方法

本提出了一个新的求解线性不等式组可行解的方法－－无约束极值方法。通过在线性不等式组的非空可行域的相对内域上建立一个非线性极值问题，根据对偶关系，得到了一个对偶空间的无约束极值及原始，对偶变量之间的简单线性映射关系，这样将原来线性不等式组问题的求解转化为一个无约束极值问题。中主要讨论了求解无约束极值问题的共轭梯度算法。同时，在寻找不等式组可行解的过程中，定义了穿越方向，这样大大减少计算量。中最后数值实验结果表明此算法是有效的。     

Minimizing the number of variable parameters for optimizing the fuzzy-controller

In the case of a few input and output variables fuzzy systems have a large number of variable parameters which make the practical design and optimization of fuzzy controllers more difficult. It is necessary to reduce the number of variable parameters to simplify the design of fuzzy controllers and to make it accessible to automated design methods. In this paper, the response characteristics and the quality of fuzzy controllers were analysed by using different variable parameters. The quality of a controller is evaluated by the deformation of the characteristic field under consideration of a similarity criterion and the Fourier analysis. It is shown that the reduction in the number of variable parameters does not necessarily result in a restriction of the quality of the fuzzy controller.     

由真值向量求异或开关函数

由于卡诺图受到变量个数的限制,在数字电路中由真值向量推求函数表达式未完美解决。在本文中,通过定义向量的两种收缩性,得到了由已知函数真值向量推求异或开关函数的简捷方法,该方法不受变量个数的限制,且易于电脑操作。     

三阶线性变系数差分方程的Mikusiski算符解法（Ⅲ）

本文在［３］，［４］工作的基础上，利用变数算符的思想以及Ｍｉｋｕｓｉｎｓｋｉ算符域中移动算符和变系数移动算符级数的有关结果，解决了一般的三阶线性变系数差分方程的求解问题，并且绘出了一些特殊的三阶线性变系数差分方程的更好的解式；此外，还试图为实现更高阶线性变系数差分方程的求解提供思想方法。     

The effects of chemical reaction,Hall and ion-slip currents on MHD flow with temperature dependent viscosity and thermal diffusivity

In this paper, the problem of magneto-micropolar fluid flow, heat and mass transfer with suction and blowing through a porous medium is analyzed numerically. This problem was studied under the effects of chemical reaction, Hall, ion-slip currents, variable viscosity and variable thermal diffusivity. The governing fundamental equations are approximated by a system of non-linear ordinary differential equation. This system is solved numerically by using the Chebyshev pseudospectral method. Details of the velocities, temperature and concentration fields as well as the local skin-friction, the local Nusselt number and the local Sherwood number for the various values of the parameters of the problem are presented. The numerical results indicate that, the concentration decreases as the permeability parameter, the chemical reaction parameter and Schmidt number increase and it increases as variable viscosity and variable thermal diffusivity increase. The local Nusselt number and the local Sherwood number decrease as the magnetic field and ion-slip current parameters increase, whereas they increase as Hall current parameter increases. Also, there is a (non-linear) strong dependency of the concentration gradient at the wall on both Schmidt number and the mass transfer parameter.     

再论保险系统的一个损失分布模型

文献［１］从理赔费是损失费的减扣额出发，给出了损失费的所有可能概率分布，但只对保险人数是一般变量的情形进行了研究．本文将保险人数视为随机变量，给出了损失费的分布，并计算了平均损失费及其方差，更具实用性     

Computational complexity of some restricted instances of 3-SAT

Tovey [A simplified satisfiability problem, Discrete Appl. Math. 8 (1984) 85-89] showed that it is NP-hard to decide the satisfiability of 3-SAT instances in which every variable occurs four times, while every instance of 3-SAT in which each variable occurs three times is satisfiable. We explore the border between these two problems. Answering a question of Iwama and Takaki, we show that, for every fixed k?0, there is a polynomial-time algorithm to determine the satisfiability of 3-SAT instances in which k variables occur four times and the remaining variables occur three times. On the other hand, it is NP-hard to decide the satisfiability of 3-SAT instances in which all but one variable occurs three times, and the remaining variable is allowed to occur an arbitrary number of times.     

属性值为区间数的变权综合决策方法

对属性值为区间数的多属性不确定性决策问题,先由区间数向量定义四组实数向量,然后利用实数状态变权向量和上述四组向量导出相应的区间数状态变权向量,由此得出区间数变权公式,进而建立区间数变权综合决策模型.最后给出一个应用区间数变权综合决策模型的实例.     

Bridge estimation for generalized linear models with a diverging number of parameters

Variable selection is fundamental to high dimensional generalized linear models. A number of variable selection approaches have been proposed in the literature. This paper considers the problem of variable selection and estimation in generalized linear models via a bridge penalty in the situation where the number of parameters diverges with the sample size. Under reasonable conditions the consistency of the bridge estimator can be achieved. Furthermore, it can select the nonzero coefficients with a probability converging to 1 and the estimators of nonzero coefficients have the asymptotic normality, namely the oracle property. Our simulations indicate that the bridge penalty is an effective consistent model selection technique and is comparable to the smoothly clipped absolute deviation procedure. A real example analysis is presented.     

变捕捞努力量收获模型控制

利用微分包含给出了努力量可变的收获模型,基于生存理论和求解线性规划给出了将单种群数量控制在某范围的方法.最后对于常用的Logistic模型,证明只要控制努力量就可以将种群数量控制在指定范围内.     

Classification accuracy in discriminant analysis: a mixed integer programming approach

Classification models can be developed by statistical or mathematical programming discriminant analysis techniques. Variable selection extensions of these techniques allow the development of classification models with a limited number of variables. Although stepwise statistical variable selection methods are widely used, the performance of the resultant classification models may not be optimal because of the stepwise selection protocol and the nature of the group separation criterion. A mixed integer programming approach for selecting variables for maximum classification accuracy is developed in this paper and the performance of this approach, measured by the leave-one-out hit rate, is compared with the published results from a statistical approach in which all possible variable subsets were considered. Although this mixed integer programming approach can only be applied to problems with a relatively small number of observations, it may be of great value where classification decisions must be based on a limited number of observations.