Two New FCT Algorithms Based on Product System

In this paper we present a product system and give a representation for consine functions with the system. Based on the formula two new algorithms are designed for computing the Discrete Cosine Transform. Both algorithms have regular recursive structure and good numerical stability and are easy to parallize.     

基于趋势关联遗传算法的系统参数辨识

在利用遗传算法的系统参数辨识中 ,利用了灰色理论中的趋势关联分析方法来构造遗传算法的适值函数 ,在适值函数的选择上兼顾了“接近性”和“相似性”的要求 ,仿真结果证明 ,本方法克服了常规遗传算法容易早熟的缺点 ,取得了满意的效果 .     

Genetic Algorithms Based on a New System of Integral Equations in Identification of Material Constants for Anisotropic Media

A hybrid method for solving inverse boundary problems is presented. The method consists in combining the genetic algorithms with a new system of integral equations. The effectiveness of the general idea of the method and its practical application are tested in the identification of material constants for a two-dimensional anisotropic medium.     

Weighted Tensor Product Algorithms for Linear Multivariate Problems

We study the ε-approximation of linear multivariate problems defined over weighted tensor product Hilbert spaces of functions f of d variables. A class of weighted tensor product (WTP) algorithms is defined which depends on a number of parameters. Two classes of permissible information are studied. Λ^all consists of all linear functionals while Λ^std consists of evaluations of f or its derivatives. We show that these multivariate problems are sometimes tractable even with a worst-case assurance. We study problem tractability by investigating when a WTP algorithm is a polynomial-time algorithm, that is, when the minimal number of information evaluations is a polynomial in 1/ε and d. For Λ^all we construct an optimal WTP algorithm and provide a necessary and sufficient condition for tractability in terms of the sequence of weights and the sequence of singular values for d=1. ForΛ^std we obtain a weaker result by constructing a WTP algorithm which is optimal only for some weight sequences.     

Two Algorithms for the Multi-Weber Problem

This paper develops two methods for finding building-blocks for solving Rosing's multi-Weber problem as a set-covering problem in zero–one programming. The building blocks are those subsets of the universe of points to be partitioned that do not contain any non-members within their own convex hulls. For a particular universe of 100 cities, there are almost six billion such subsets, and the paper sets out computational methods that make this enumeration feasible. Some of these methods have wider applications, but the central methods are closely tailored to this problem. Means are also suggested for reducing the number of subsets to be enumerated, without ruling out possibly optimal solutions for the complete problem.     

Primal-dual Interior-point Algorithms for Second-order Cone Optimization Based on a New Parametric Kernel Function

A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O（√Nlog N log N/ε） for large-update methods and O（√Nlog N/ε） for smallupdate methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q.     

统计缺省扩充的两种算法

讨论统计缺省理论的扩充,它是经典缺省逻辑(R e iter缺省)的推广,它借助错误参数ε,允许我们在标准的推理统计中模型化普遍的推理模式。由于统计缺省扩充不具备封闭性,在其对应的R e iter扩充存在时,它的扩充可能不存在;甚至可能出现正规的统计缺省理论没有扩充的情形。但是如果给出一定的限制条件,就可以克服这一缺陷。本文给出了在这种限制条件下,统计缺省理论扩充的两种计算方法。     

基于免疫算法的组合预测方法

利用免疫算法搜索全局最优解能力,提出了一种其于免疫算法的组合预测权系数确定的新方法,并给出了具体算法.仿真实验结果表明了免疫算法在组合预测方面具有很好的可行性和有效性.     

New Theoretical Results on Recursive Quadratic Programming Algorithms

Recursive quadratic programming is a family of techniques developed by Bartholomew-Biggs and other authors for solving nonlinear programming problems. The first-order optimality conditions for a local minimizer of the augmented Lagrangian are transformed into a nonlinear system where both primal and dual variables appear explicitly. The inner iteration of the algorithm is a Newton-like procedure that updates simultaneously primal variables and Lagrange multipliers. In this way, as observed by Gould, the implementation of the Newton method becomes stable, in spite of the possibility of having large penalization parameters. In this paper, the inner iteration is analyzed from a different point of view. Namely, the size of the convergence region and the speed of convergence of the inner process are considered and it is shown that, in some sense, both are independent of the penalization parameter when an adequate version of the Newton method is used. In other words, classical Newton-like iterations are improved, not only in relation to stability of the linear algebra involved, but also with regard to the ovearll convergence of the nonlinear process. Some numerical experiments suggset that, in fact, practical efficiency of the methods is related to these theoretical results.     

Special Points on the Product of Two Modular Curves

We prove, assuming the generalized Riemann hypothesis for imaginary quadratic fields, the following special case of a conjecture of Oort, concerning Zarsiski closures of sets of CM points in Shimura varieties. Let X be an irreducible algebraic curve in C², containing infinitely many points of which both coordinates are j-invariants of CM elliptic curves. Suppose that both projections from X to C are not constant. Then there is an integer m 1such that X is the image, under the usual map, of the modular curve Y₂0(m). The proof uses some number theory and some topological arguments.     

两个图的积的S-不可收缩性(英)

本文从组合角度明确给出了两个图的积是S-不可收缩的特征．     

Local Algorithms for the Prime Factorization of Strong Product Graphs

The practical application of graph prime factorization algorithms is limited in practice by unavoidable noise in the data. A first step towards error-tolerant “approximate” prime factorization, is the development of local approaches that cover the graph by factorizable patches and then use this information to derive global factors. We present here a local, quasi-linear algorithm for the prime factorization of “locally unrefined” graphs with respect to the strong product. To this end we introduce the backbone \mathbbB (G)\mathbb{B} (G) for a given graph G and show that the neighborhoods of the backbone vertices provide enough information to determine the global prime factors.     

Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems

We study multivariate tenser product problems in the worst case and average case settings. They are defined on functions of d variables. For arbitrary d, we provide explicit upper bounds on the costs of algorithms which compute an ϵ-approximation to the solution. The cost bounds are of the form (c(d) + 2)β₁(β₂ + β₃(ln 1/ϵ)/(d − 1))^{β₄(d − 1)}(1/ϵ)^β₅. Here c(d) is the cost of one function evaluation (or one linear functional evaluation), and β_i′s do not depend on d; they are determined by the properties of the problem for d = 1. For certain tensor product problems, these cost bounds do not exceed c(d)Kϵ^−p for some numbers K and p, both independent of d. However, the exponents p which we obtain are too large. We apply these general estimates to certain integration and approximation problems in the worst and average case settings. We also obtain an upper bound, which is independent of d, for the number, n(ϵ, d), of points for which discrepancy (with unequal weights) is at most ϵ, n(ϵ, d) ≤ 7.26ϵ^−2.454, ∀d, ϵ ≤ 1.     

新产品设计前端的筛选与评价系统研究

本着重于新产品设计前端的筛选与评价系统研究。设计了若干准则，有社会环境准则、经济成本准则、技术准则、时间准则、价值准则等，对新产品构思进行筛选。运用模糊理论，确定隶属度函数，得到评价矩阵，最终得到综合评价；运用加权评分法，确定评判的各影响因素及其各自所占的权重，给每种构思进行评分，根据最后总得分的多少来评定构思的优劣。最后，阐述了评价系统在设计过程中的重要作用，评价系统贯穿于整个设计过程中。     

Minimization Algorithms Based on Supervisor and Searcher Cooperation

In the present work, we explore a general framework for the design of new minimization algorithms with desirable characteristics, namely, supervisor-searcher cooperation. We propose a class of algorithms within this framework and examine a gradient algorithm in the class. Global convergence is established for the deterministic case in the absence of noise and the convergence rate is studied. Both theoretical analysis and numerical tests show that the algorithm is efficient for the deterministic case. Furthermore, the fact that there is no line search procedure incorporated in the algorithm seems to strengthen its robustness so that it tackles effectively test problems with stronger stochastic noises. The numerical results for both deterministic and stochastic test problems illustrate the appealing attributes of the algorithm.     

两类网页重要性排序算法的概率对比

PageRank和BrowseRank算法是近年来针对网页重要性排序提出的两类典型算法.本文基于更新过程,通过遍历理论分析对比两类网页重要性排序算法,发现它们都利用随机游走的思想来模拟用户在互联网上浏览网页的行为,不同的是前者是离散时间参数的马尔可夫链而后者是连续时间参数的.而且它们所利用的数据也不同,前者基于网络链接图而后者是从真实用户浏览日志中生成的用户浏览图.此外,我们还证明随机游走的平稳分布是对网页重要性的一个合理且可行的衡量方法,并给出目前一些文献中所获得的实验结果的概率解释和意义.     

一个整数瓶颈问题的两个多项式算法

讨论下列数学模型Ⅰ:求x=(x_1,x_2,…,x_n)适合条件{■a_(ij)x_j≥b_i (i=1,2,…,m) x_j≥0且整数(j=1,2,…,n)使f(x)■{c_jx_j}达到最小值,其中m＜n,a_(ij),b_i及c_j均为正整数。对该模型,建立了两个多项式算法,其复杂度均为O(n~2),并列举了一个数值例子．     

On the Linear Convergence of Two Decentralized Algorithms

Journal of Optimization Theory and Applications - Decentralized algorithms solve multi-agent problems over a connected network, where the information can only be exchanged with the accessible...