数学规划方法确定的最优生产函数的性质

§1.最优生产函数的存在性 令R_+~n={(x_1,…,x_n)|x_i≥0,i=},设生产过程的投入向量为x∈XR_+~n(X为投入可能集),产出向量为y∈R_+~m,已知生产活动观测集为:={(x~1,y~1),…,(x~N,y~N)}其中x~i∈R_+~n,y~i∈R_+~m,x~i≠0(0,0),i=,那么由诱导的生产可能集为:     

零售商合作偏好下生鲜农产品供应链的政府补贴机制与优化策略

在零售商具有合作偏好行为的背景下,针对自然灾害影响产出的特性,设计基于“优先保证最大化社会福利的基础上促进农户增收”的灾害年的不同政府补贴政策,建立了政府、零售商和农户的三阶段Stackelberg博弈模型.对比分析了政府的不同补贴政策以及零售商的合作偏好行为对政府的最优补贴率、零售商的最优收购价格、农户的最优生产投入量和三方利益的影响,并给出了政府的最优补贴政策。研究结果表明:(1)当零售商的合作偏好程度低于某一临界值,且“丰收年”发生的概率适中或偏高时,政府的最优补贴政策是对农户提供补贴;否则,政府的最优补贴政策是对零售商提供补贴;(2)政府的补贴政策可以实现政府、消费者和未受补贴方三方共赢的局面,但获补贴方不一定增收。     

广告媒介下互补产品市场扩散扰动模型研究

创新产品通过广告媒介来传递信息以提高市场需求,对产品的扩散起着一定的作用.将创新产品的互补性分为三类互补类型,即两种产品均有独立的市场,两个产品均无独立市场,只有一个产品有独立市场.分别建立广告媒介下具有互补关系的创新产品扩散动态模型,分析具有不同竞争力的创新产品具有互补关系时市场的稳定状态,解释了产品互补型的企业纵向兼并及合用的原因,为模拟和预测动态市场结构演变及管理决策提供了理论依据.     

基于核函数求解线性互补问题的不可行内点算法

本文研究了线性互补问题内点算法.利用全牛顿步长求解迭代方向,获得了算法迭代复杂性为O(nlogn/ε),推广了Roos等关于线性规划问题不可行内点算法,其复杂性与目前最好的不可行内点算法复杂性一致.     

基于AHP-GRA的湖北省科技创新人才开发评价研究

科技创新人才是推动经济社会发展的核心资源,是提升一个区域乃至一个国家核心竞争力的关键所在.以科技创新人才开发为核心,从人才可持续发展的视角,建立一套衡量湖北省科技创新人才开发水平的评价指标体系,同时结合层次分析法(AHP)和灰色关联分析法(GRA)构建评价模型,对湖北省科技创新人才开发水平及发展态势进行实证分析,探索提高湖北省科技创新人才开发水平的对策建议,为湖北省制定科技人才开发战略以及加强科技人才队伍建设提供决策参考.     

Evolutionary games in a generalized Moran process with arbitrary selection strength and mutation

By using a generalized fitness-dependent Moran process, an evolutionary model for symmetric 2×2 games in a well-mixed population with a finite size is investigated. In the model, the individuals' payoff accumulating from games is mapped into fitness using an exponent function. Both selection strength β and mutation rate ε are considered. The process is an ergodic birth-death process. Based on the limit distribution of the process, we give the analysis results for which strategy will be favoured when ε is small enough. The results depend on not only the payoff matrix of the game, but also on the population size. Especially, we prove that natural selection favours the strategy which is risk-dominant when the population size is large enough. For arbitrary β and ε values, the 'Hawk--Dove' game and the 'Coordinate' game are used to illustrate our model. We give the evolutionary stable strategy (ESS) of the games and compare the results with those of the replicator dynamics in the infinite population. The results are determined by simulation experiments.     

THE AVERAGE ABUNDANCE FUNCTION WITH MUTATION OF THE MULTI-PLAYER SNOWDRIFT EVOLUTIONARY GAME MODEL

This article explores the characteristics of the average abundance function with mutation on the basis of the multi-player snowdrift evolutionary game model by analytical analysis and numerical simulation.The specific field of this research concerns the approximate expressions of the average abundance function with mutation on the basis of different levels of selection intensity and an analysis of the results of numerical simulation on the basis of the intuitive expression of the average abundance function.In addition,the biological background of this research lies in research on the effects of mutation,which is regarded as a biological concept and a disturbance to game behavior on the average abundance function.The mutation will make the evolutionary result get closer to the neutral drift state.It can be deduced that this affection is not only related to mutation,but also related to selection intensity and the gap between payoff and aspiration level.The main research findings contain four aspects.First,we have deduced the concrete expression of the expected payoff function.The asymptotic property and change trend of the expected payoff function has been basically obtained.In addition,the intuitive expression of the average abundance function with mutation has been obtained by taking the detailed balance condition as the point of penetration.It can be deduced that the effect of mutation is to make the average abundance function get close to 1/2.In addition,this affection is related to selection intensity and the gap.Secondly,the first-order Taylor expansion of the average abundance function has been deduced for when selection intensity is sufficiently small.The expression of the average abundance function with mutation can be simplified from a composite function to a linear function because of this Taylor expansion.This finding will play a significant role when analyzing the results of the numerical simulation.Thirdly,we have obtained the approximate expressions of the average abundance function corresponding to small and large selection intensity.The significance of the above approximate analysis lies in that we have grasped the basic characteristics of the effect of mutation.The effect is slight and can be neglected when mutation is very small.In addition,the effect begins to increase when mutation rises,and this effect will become more remarkable with the increase of selection intensity.Fourthly,we have explored the influences of parameters on the average abundance function with mutation through numerical simulation.In addition,the corresponding results have been explained on the basis of the expected payoff function.It can be deduced that the influences of parameters on the average abundance function with mutation will be slim when selection intensity is small.Moreover,the corresponding explanation is related to the first-order Taylor expansion.Furthermore,the influences will become notable when selection intensity is large.     

非可微分二层Lipschitz规划的广义微分和广义方向导数

本文对构成函数为Ｌｉｐｓｃｈｉｔｚ函数的二层规划问题,利用非光滑分析工具,讨论了下层极值函数和上层复合目标函数的Ｌｉｐｓｃｈｉｔｚ连续性,给出了这些函数的广义微分和广义方向导数的估计式。本文得到的结果为进一步研究非可微二层Ｌｉｐｓｃｈｉｔｚ规划的最优性条件和有效算法等理论和方法问题奠定了基础。     

基于混合支持向量机的国防R&D项目中止决策方法

由于RD活动的高风险性,对国防RD项目开展中止决策研究具有重要的理论和现实意义.将传统RD项目中止决策的解决途径分为两类:分类型和回归型.在分析这两种解决途径存在不足的情况下,考虑到国防RD项目自身的特点,提出一种基于混合支持向量机(support vector machine,SVM)的项目中止决策方法;同时,针对模型的建立问题,提出采用交叉验证的方法,通过粒子群优化(particle swarm optimization,PSO)算法实现模型的优化选择.通过建立混合决策模型,可以得出项目中止决策的明确结论.应用分析表明,该方法能够同时实现对项目的分类和排序,较常用方法利用信息更为全面,得出结论更为细致,对实践中的项目中止决策具有较好的适应性.