A globally convergent BFGS method for pseudo-monotone variational inequality problems

In this paper, we propose a globally convergent BFGS method to solve Variational Inequality Problems (VIPs). In fact, a globalization technique on the basis of the hyperplane projection method is applied to the BFGS method. The technique, which is independent of any merit function, is applicable for pseudo-monotone problems. The proposed method applies the BFGS direction and tries to reduce the distance of iterates to the solution set. This property, called Fejer monotonicity of iterates with respect to the solution set, is the basis of the convergence analysis. The method applied to pseudo-monotone VIP is globally convergent in the sense that subproblems always have unique solutions, and the sequence of iterates converges to a solution to the problem without any regularity assumption. Finally, some numerical simulations are included to evaluate the efficiency of the proposed algorithm.     

四维空间直线绕平面的旋转

本文对四维空间直线绕平面旋转的轨迹进行一投详尽的讨论，按照直线与“轴平面”的相对位置不同，该旋转轨迹分别为圆柱面、圆锥面和单叶回转双曲面，并认为这些回转曲面的轴线是过该直线的与“轴平面”垂直的超平面与“轴平面”的交线。     

Pseudoinverse in clustering problems

The clustering of vector observations of hyperplanes is studied. Different cases of correspondence distances are proposed and investigated, including the algebraic Jack Knife one. The efficiency, constructivity, and explicit form of formulas are provided by using the pseudoinverse technique including the pseudoinverse-perturbation theory. Results important for the application of pseudoinverse and related operators are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 73–92, July–August 2007.     

基于线性判别边信息结合PHL的三维人脸识别

针对三维人脸识别中受光照、姿态、表情等变化而影响识别性能的问题,提出了一种原型超平面学习算法。利用SVM将弱标记数据集中的每个样本表示为一个原型超平面中层特征,使用学习组合系数从未标记的通用数据集中选择支持向量稀疏集;借助于Fisher准则最大化未标记数据集的判别能力,使用迭代优化算法求解目标函数;利用SILD进行特征提取,余弦相似性度量完成最终的人脸识别。在USCD/Honda、FRGC v2、LFW及自己搜集的人脸数据集上的实验结果表明,该算法优于其他几种三维人脸识别算法。     

稳健二进神经网络的几何训练

在二进神经网络的规划划分训练方法基础上,针对稳键二进神经网络稳健神经元的特点,讨论了稳健分类超平面的几何构造方法,并提出了相应的训练算法,包括隐层神经元的几何训练和输出神经无的进化训练。实验表明,该算法对复杂Boole函数的稳健二进神经网络的实现是有效且可行的。     

On the number of term orders

By an admissible order on a finite subsetQ of ⁿ we mean the restriction toQ of a linear order on ⁿ compatible with the group structure of ⁿ and such that ⁿ is contained in the positive cone of the order. We first derive upper and lower bounds on the number of admissible orders on a given setQ in terms of the dimensionn and the cardinality ofQ. Better estimates are possible if the setQ enjoys symmetry properties and in the case whereQ is a discrete hyperbox of the form In the latter case, we also give asymptotic results as d _k for fixedn. We finally present algorithms which compute the set of admissible orders that extend a given binary relation onQ and their number. The algorithms are useful in connection with the construction of universal Gröbner bases.AMS Classification: primary 06F20 secondary 06-04, 11N25     

支持向量机在网络故障诊断中的应用研究

支持向量机是一种解决小样本、非线性、高维问题的机器学习算法，它为网络故障诊断向智能化方向发展提供了新的途径。介绍了支持向量机的基本原理，并且以实验网中采集的数据为例进行了实验，对实验过程和结果进行了说明和分析。     

计算机图解计算线性规划问题

本文运用多维画法几何的理论和人机对话的方式,对于四元线性规划问题,通过图解计算可以快速、准确地求出其最优解.     

四维超二次平面纹曲面的探讨

本文提出了四维空间中平面纹超曲面的形成条件,并证明了与不共超平面的两个平面和一条直线分别共超平面的平面轨迹是一个秩4的超二次平面纹曲面,或者与属于一点的三个平面均共超平面的平面轨迹亦是一个秩4的超二次平面纹曲面,且形成超二次曲面的这两种条件是等价的.文中还对这种超二次曲面的性质作了详细讨论。     

变结构控制系统的基本理论,应用及发展现状

本文详细介绍了变结构系统 (VSS)的基本理论 ,变结构系统在实际中的应用及 VSS的发展现状