基于MATLAB的无约束优化问题对称秩-1法与BFGS法之探讨

对称秩-1法和BFGS法是用拟牛顿法求解无约束优化问题时最常见的两种方法,它们都具有计算简单、收敛速度快等优点.探讨两种方法的算法格式、收敛速度和计算精度问题,同时利用MATLAB软件编程进行实例求解.结果表明:在解的迭代次数和精确度方面,BFGS算法均明显优于对称秩-1法.     

序列二次规划中迭代矩阵的正定性研究

将Li-Fukushima(2001)提出的求解无约束最优化问题的BFGS公式应用于求解约束最优化问题的序列二次规划算法.该修正公式的显著优点在于二次规划子问题是一个严格凸二次规划问题,而且二次规划的解是许多效益函数的下降方向.在较弱的条件下,我们得到了算法的全局收敛性.     

投影迭代算法求解反双障碍问题

本文研究了求解双松弛投影迭代算法求解反双障碍问题,并证明了此算法所产生的迭代点列至少存在一个聚点,该聚点即是反双障碍问题的解.而且,当矩阵为非退化的对称矩阵时,该点列收敛到反双障碍问题的解.     

投影ESOR迭代求解双边障碍问题

在本文中我们研究了求解双边障碍问题的ESOR迭代算法.证明了由此算法产生的迭代序列至少存在一个聚点,该聚点是双边障碍问题的解.并且,当矩阵为非退化对称矩阵时,该序列收敛到双边障碍问题的解.     

双松弛迭代算法求解一类对称双正型线性互补问题

文章为求解一类对称双正型的线性互补问题而建立了一种投影前迭代和投影后迭代的双松弛迭代算法.并给出了此算法所产生的迭代序列的聚点是该互补问题的解.而且当该问题中的矩阵为对称双正加矩阵或者严格对称双正矩阵时,由该算法所得的迭代序列一定存在子列收敛到该问题的解.若该问题中的矩阵为非退化的对称双正加矩阵时,所得序列一定收敛.     

一种基于弱拟牛顿方程的对角拟牛顿法

基于弱拟牛顿方程,结合Armijo非精确线性搜索设计了一种求解大规模无约束优化问题的对角拟牛顿法,该算法在每次迭代时利用对角矩阵逼近Hessian矩阵,使计算搜索方向的存储量和工作量明显减少.在一定的假设条件下,证明了算法的全局收敛性和R-线性收敛性.通过数值实验表明该算法是有效的,适于求解大型无约束优化问题.     

分裂变分不等式问题及其外梯度算法

在本文中,我们结合Armijo步长搜索方法提出了求解分裂变分不等式问题的一种外梯度算法,证明了算法的收敛性．与相关文献中的算法相比,该算法避免了矩阵谱半径的计算．     

正则化低秩子空间谱聚类算法

为解决缺损数据谱聚类中的不适定问题,提出一种正则化低秩子空间谱聚类算法。首先根据数据集建立核范数正则化低秩矩阵分解模型,然后用迭代法求解模型得出系数矩阵,由此构造相似矩阵,最后利用谱聚类算法得出聚类结果。实验表明,该算法在一定程度上可以解决缺损数据的谱聚类问题,抑制噪声,获得质量较高的聚类结果。     

基于Newton法改进的BFGS迭代算法与Newton-CG算法

本文主要研究了数值分析中数值优化与非线性方程组求解这两个重要问题.文中首先概述了数值优化与非线性方程组的关系,然后对BFGS法的算法公式进行了改进,并对非线性方程组求解问题提出了一种改进的算法——Newton-CG算法.     

求解线性不适定问题的压缩投影加速迭代算法

考虑求解线性不适定问题的多尺度压缩投影算法,采用具有矩阵压缩策略的多尺度Galerkin方法,对Nesterov加速后的Landweber迭代正则化方程进行离散,给出近似解的先验误差估计,并提出后验参数选择策略,确保近似解的最优收敛率.数值实验表明将Nesterov加速方案应用到有限维空间求解线性不适定问题时,Landweber迭代速度明显加快.     

分块压缩存储的追赶算法及并行计算

本文提出了以分块压缩存储形式直接求解拟块三角方程组的分块追赶法及其并行计算方案,本算法计算精度高、速度快、并行性好可求解问题规模大,是直接求解此类问题的一个有效算法.     

An enhanced landscape aggregation index

The aggregation index (AI) is a classical ecology calculation method, which has been widely used for measuring the aggregation level of spatial patterns within a landscape scale in landscape ecological studies. However, it has certain limitions. For instance, identical results can be obtained by AI even when the shape and number of landscape patches are totally different in two landscape units. Furthermore, the value of AI approaches to 1 if the landscape patch is large enough. To solve these problems, a logical limitation of the original AI equation was revised firstly. Secondly, an improved AI-J was developed based on the awareness of the effects of spatial distribution characteristics of patches and changing spatial scale on AI operation. Finally, the accuracy of AI and AI-J results were evaluated through a case study of city green patches in Chengdu, P. R. China. The results show that the calculated result of AI-J is more precise than that of AI and AI-J can be used to compare a certain landscape class under different spatial scales.     

Non-interior continuation algorithm for solving system of inequalities over symmetric cones

As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.     

Simulation study of item bias detection with restricted factor analysis

Restricted factor analysis (RFA) can be used to detect item bias (also called differential item functioning). In the RFA method of item bias detection, the common factor model serves as an item response model, but group membership is also included in the model. Two simulation studies are reported, both showing that the RFA method detects bias in 7‐point scale items very well, especially when the sample size is large, the mean trait difference between groups is small, the group sizes are equal, and the amount of bias is large. The first study further shows that the RFA method detects bias in dichotomous items at least as well as an established method based on the one‐parameter logistic item response model. The second study concerns various procedures to evaluate the significance of two‐item bias indices provided by the RFA method. The results indicate that the RFA method performs best when it is used in an iterative procedure.     

一类三阶微分方程边值问题的渐近解

讨论了一类三阶微分方程奇摄动边值问题.根据奇摄动理论得知问题的解在左边界点邻近具有非一致性.为构造一致有效的渐近解,利用多重尺度法.引进一个适当的快变量.把原来单个自变量的常微分方程转化为两个尺度变量的偏微分方程,再将解按两尺度变量展开成幂级数形式,并将这个幂级数展开式代入原问题的方程中,合并同量级的系数并令其为零.再利用原问题的边界条件和关于小参数的渐近展开原理及消去长期项的办法.可依次决定各待定量,从而克服了原问题解的展开式的非一致收敛性.最后得到了关于原三阶微分方程边值问题的一阶小量的一致有效的渐近解.     

有限差分法在一维输运方程定解中的运用

有限差分方法就是一种数值解法,在一维输运方程定解中可以巧用它来解题,把表示变量连续变化关系的偏微分方程离散为有限个代数方程,然后利用电子计算机求此线性代数方程组的解。     

Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem

INTRODUCTION The vehicle routing problem (VRP), which was first introduced by Dantzig and Ramser (1959), is a well-known combinatorial optimization problem in the field of service operations management and logis- tics. The capacitated vehicle routing problem (CVRP) is an NP-hard problem for simultaneously determining the routes for several vehicles from a central depot to a set of customers, and then return to the depot without exceeding the capacity constraints of each vehicle. In pr…     

河南省高校声乐教育存在的问题及应对策略

河南省是声乐教育大省,却不是声乐教育强省,目前仍存在着如生源质量逐年下滑,选修课程偏少,漠视流行歌曲演唱,师生比过分悬殊和单向度教学等招生、教学内容、教学方式方法层面的诸多问题。认识问题是为了更好地解决问题,诸如收紧招生规模,调整招生层次,提高选修课比重,加强与市场需求接轨的流行音乐学科建设等应对策略的提出便是如此。     

研究生规模与结构问题研究

规模与结构问题是由研究生教育的社会适应性质量和社会资源配置绩效问题衍生出的问题.研究生教育的规模与结构是社会理性与价值综合作用的产物,不可能存在"精确"的量化数据.国家层面的集中调控不是问题解决的最佳途径,劳动力市场信息与教育信息的全面、科学建设,学位授权审核制度科学合理的发展更可能形成一个有效的调节机制,使研究生教育...     

中国"三农"的无解、难解、必解与破解

“三农问题”中有些问题，按目前的认识水平，是无法解决的；有的问题，受条件限制，很难解决。但农村资源低效利用，县乡政权人员膨胀、机构臃肿，农村金融市场，社会保障，农民进城等问题，必须解决，而且又非解决不可。破解的方法只有从打破“小农经济基础”开始，进行一系列制度创新，农业规模化经营和人口向城市转移，同时进行，农村的繁荣不是没有可能的。