计算机高级语言在数值分析中的应用——浅谈在计算机上实践一元非线性方程求根的方法

我们知道，数值分析也称做计算方法，它主要是研究各种数学物理问题求解的数值计算方法，对于数值计算方法包括内容很多，像函数数值逼近、数值微分和数值积分、方程求近似解等等，在这里我们就浅谈其中的一种，简单介绍一下一元非线性方程求近似解的方法问题。下面我们将要给出一元非线性方程求根的几种数值计算方法。     

新产品开发合作伙伴的优化选择研究

研究新产品开发项目中的合作伙伴选择问题,用带有非线性目标函数的0-1整数规划模型对问题进行定量描述,在时间和成本约束下的最小化项目失败风险。模型的非线性和复杂性使其无法用常规方法进行求解,设计带有自适应惩罚函数的遗传算法对可行域和非可行域进行搜索,快速有效地获得最优解或近优解。     

工程网络计划最低费用工期的一种优化方法

一、问题的提出计算最低费用工期是工程项目计划网络中的优化问题之一。目前,对网络最低费用工期的优化方法有比较多的研究,且取得了一定进展。但每一类方法都有相应的适用范围,显现一定局限性。如枚举法虽直观简单,但对大型网络难以应用;数学规划法依据所给条件构建线性规划模型,能在计算机上运算,适用于大型网络的寻优求解,但缺乏应用的灵活性;试探性算法没有确定性计算程序,存在遗漏最优解的可能。本文将一个建设项目的网络图划分为若干工序时段,通过每一时段的费用比较,按既定程序逐步缩短计划工期,进而确定整个网络最低费…     

基于种子优化算法的救灾物资调度优化问题的研究

研究在救灾物资调度中,建立物资调度问题的数学模型,运用种子优化算法的思想求解该问题,并进行了实验计算。计算结果表明,用种子优化算法解决救灾物资调度问题,可以方便、快速地求得最优解或近似最优解。     

考虑次关键路线的基于粒子群算法工期-费用优化研究

工期-费用优化是网络优化技术的核心内容。传统的工期-费用优化研究忽略了次关键路线、资源约束条件对工期压缩的影响。本文研究了次关键路线对工期压缩的影响,描述了求解最低压缩成本的特征路线法,并以此为基础建立了有资源约束的工期-费用优化数学模型。对解进行编码处理后,采用粒子群算法对工期费用优化模型进行求解,并根据求得的最优解来调整工序工期,最终实现工期-费用的最优化。最后,经过工程实例的仿真,证明了模型的合理性和有效性。     

线性规划常见问题例析

在线性约束条件下求线性目标函数的最大值或最小值问题,通常称为线性规划问题,求解线性规划这类问题的步骤为：①画：画线性约束条件所表示的可行域及目标函数线;②移：平移目标函数线,确定其平行线中与可行域有公共点且截距最大或最小的直线所经过的可行域内的点;③求：解方程组求出最优解;④答：写出答案．下面就线性规划问题的试题形式举例,同大家交流．     

对偶定理在运输问题中的应用

运输问题是一类重要的线性规划问题,这类问题是求解某种物资从若干个产地至若干个销地的最小运费及最优方案。各产地、销地的供、需量作为已知前提。根据运输问题数学模型本身的特点,人们提供了不同的解法。加深了对共轭泛函与对偶理论的认识,系统介绍了最优化理论中各种形式运输问题的不同的数学模型,并将其化简为平衡运输问题的数学模型,再利用对偶定理,对各种模型进行了求解化简,使之成为单变量的优化问题,这样能更容易求出运输问题具体的解。     

线性问题与非线性问题算子方程近似解法浅析

本文结合相关文献综述了算子方程近似解法的各种稳定性和收敛性理论,在其过程中也渗透了稳定性和收敛性的关系,最后对线性问题与非线性问题算子方程近似解法浅析.     

CPM网络中单工序对时差的敏感性分析

CPM网络计划中,机动时间是网络计划管理的一个核心概念.计算和利用机动时间是网络计划技术中的一个重要问题,它为计划进度的安排提供了选择的可能性,同时为求得计划安排和资源分配提供合理方案.通过对机动时间的研究,引入了总时差、安全时差、自由时差、干扰时差、节点时差等各种网络时差的概念.某一工序对机动时间的使用可能会对其它工序的各类时差产生影响,使网络各类时差的总量发生变化.单工序对网络时差的敏感性分析就是量化该影响效果.针对该问题,提出特征值参量的概念和计算方法,利用该参量分别分析了单工序对网络总时差、网络安全时差、网络自由时差和网络节点时差的敏感性,列出了单工序机动时间使用量和网络各时差所受影响程度之间的函数关系,并分析了其正确性.最后,结合应用举例进行了具体阐述.     

优化试解原理

在工程实践中,有些超越函数的极值或根无法直接求解、或用迭代方法求解,不得不采用试解的方法来完成,本文通过试解来表明在编写工程计算程序中经常用到.     

Heterogeneous technology and the technological catching-up hypothesis: Theory and assessment in the case of MENA countries

Long run convergence implies that the convergence hypothesis will be rejected if the income differential is not stationary. However, this definition is valid only if the catching-up process between the two countries is already over. If we take into account catching-up dynamics, then poorest countries should obtain a faster growth than developed countries. Thus, income gaps should integrate decreasing time trends. We formalise this hypothesis theoretically using a stochastic neoclassical growth model with heterogeneous technology. We then apply this model to the issue of per-capita GDP catching-up of eight MENA countries towards the level of income in Europe. We approximate the nonlinear deterministic trend by a linear function with breaks and apply panel unit root tests with breaks. The analysis reveals firstly that the periods of divergence outnumber the periods of convergence. Secondly, since the year 2000 all countries but Syria have been converging toward the European per-capita income level.     

Interval programming model for risk-based partner selection of virtual enterprise

The problem of risk-based partner selection of virtual enterprise is investigated. By choosing optimal partner for each project task, the project risk is minimized. The risk parameters are expressed in the form of interval numbers when the precise values are difficult to obtain, and the model is formulated into a 0-1 nonlinear programming with interval coefficients in its objective function. In order to solve the problem, the definition of order relation between interval numbers is given, and the original model is converted into an equivalent crisp bi-objective programming model. Because of the highly constrained nature and multiple objective of the model, a genetic algorithm is proposed to find the set of Pareto or near Pareto optimal solutions. The approach is demonstrated by some numerical examples, and the result shows that the suggested approach has high efficiency and the model has potential to practical applications.     

Approximate efficiency in repeated games with correlated private signals

This paper presents repeated games with hidden moves, in which players receive imperfect private signals and are able to communicate. We propose a conditional probability approach to solve the learning problem in repeated games with correlated private signals and delayed communication. We then apply this approach to symmetric n-player games to obtain an approximate efficiency result.     

Linear economies are “gross substitute” systems

The uniqueness of the equilibrium price in linear exchange economies is proved by exploiting their “gross substitute” properties. A necessary and sufficient condition for the uniqueness is that no equilibrium price decomposes the economy. By a familiar mathematical tool — restriction and projection, the demand correspondence becomes a smooth function. We can then apply properties of the Jacobian matrix, which always has a dominant or quasi-dominant diagonal. The combination of convex and differential analysis can be used in piecewise linear economies. The uniqueness of the equilibrium price is a special case of the equilibrium index formula for regular piecewise linear economies.     

Cooperative research,government involvement,and timing of innovations

Government involvement in the innovation process, both direct and indirect, is introduced into a standard innovation time-cost trade-off model. Different forms of involvement are treated and each form entails cooperation between the firm and the government. The optimal development time (or project completion date) is determined and analyzed parametrically. This analysis produced five hypotheses concerning the effect of government involvement on the timing of innovations. Selected empirical applications (or tests) of the hypotheses are presented and then concluding remarks are made.     

Generalized cointegration: a new concept with an application to health expenditure and health outcomes

We propose a new generalization of the concept of cointegration that allows for the possibility that a set of variables are involved in an unknown nonlinear relationship. Although these variables may be unit-root non-stationary, there exists a nonlinear combination of them that takes account of such non-stationarity. We then introduce an estimation technique that allows us to test for the presence of this generalized cointegration in the absence of knowledge as to the true nonlinear functional form and the full set of regressors. We outline the basic stages of the technique and discuss how the issue of unit-root non-stationarity and cointegration affects each stage of the estimation procedure. We then apply this technique to the relationship between health expenditure and health outcomes, which is an important but controversial issue. A number of studies have found very little or no relationship between the level of health expenditure and outcomes. In econometric terms, if there is such a relationship, then there should exist a cointegrating relationship between these two variables and possibly many others. The problem that arises is that we may be either unable to measure these other variables or that we do not know about them, in which case we may incorrectly find no relationship between health expenditures and outcomes. We then apply the concept of generalized cointegration; we obtain a highly significant relationship between health expenditure and health outcomes.     

Theory and Application of Linear Supply Function Equilibrium in Electricity Markets

We consider a supply function equilibrium (SFE) model of interaction in an electricity market. We assume a linear demand function and consider a competitive fringe and several strategic players having capacity limits and affine marginal costs. The choice of SFE over Cournot equilibrium and other models and the choice of affine marginal costs is reviewed in the context of the existing literature. We assume that bid rules allow affine or piecewise affine non-decreasing supply functions by firms and extend results of Green and Rudkevitch concerning the linear SFE solution. An incentive compatibility result is proved. We also find that a piecewise affine SFE can be found easily for the case where there are non-negativity limits on generation. Upper capacity limits, however, pose problems and we propose an ad hoc approach. We apply the analysis to the England and Wales electricity market, considering the 1996 and 1999 divestitures. The piecewise affine SFE solutions generally provide better matches to the empirical data than previous analysis.     

基础设施PPP模式融资结构优化研究

公私合作模式（PPP模式）越来越多地应用于基础设施建设当中,并逐渐成为解决大型准营利性基础设施融资难题的有力方式。本文首先对PPP辛莫式内涵、应用范围、融资过程进行了剖析,肯定PPP;fJ~式融资优势的同时提出了其应用问题。其次建立了基于蒙特卡洛技术的融资结构优化模型,并对主要影响因素及其作用机理进行了分析。最后通过一个简化算例展示了模型的使用过程,证明了仿真模型的有效性。该模型在融资初期即考虑风险的合理分担,为融资谈判提供了一个较好的基准点,有利于缩短谈判时间、降低融资费用、提高PPP模式的使用效率。同时,通过仿真模型优化GPPP项目融资结构,有利于决策者找到满意的融资结构。     

基于系统动力学模型的铁路建设项目宏观经济效益评价

系统动力学采用系统仿真方法进行长期动态模拟,不受描述方程的高阶非线性限制,也不受数据不完全的影响,且处理问题直观形象,便于人机对话。本文将系统动力学与区域经济-交通系统相结合,建立了铁路建设项目宏观经济效益评价的系统动力学模型,并对模型进行了合理性检验,证明了系统动力学方法在铁路建设项目宏观经济效益评价中具有可操作性和推广价值。