分段线性凸费用网络流的两个算法

本文讨论了分段线性凸费用网络流问题,推广了线性费用网络流中的负回路方法和最小费用路方法,从而得到了求分段线性凸费用网络的最小费用流的两个算法。     

保形的Hermite插值样条函数

本文讨论一种满足Hermite 插值条件的保形样条函数,文中构造了一个保单调的样条函数q(x),且q(x)满足下列条件:1)q(x_i)=y_i,i=0,1,2,…,n,n+1;2)q'(x_i)=y'_ii=0,1,2,…,n,n+1.该方法对凸数组及相应的导数也适合。     

Constructing a strict total order for alternatives characterized by multiple criteria: An extension

The problem of finding a strict total order for a finite set of multiple criteria alternatives is considered. Our research extends previous work by us, which considered finding a partial order for a finite set of alternatives. We merge the preference information extracted from the preference cones and corresponding polyhedral sets, with the information derived from pairwise comparisons of two alternatives, yielding a preference matrix. This preference matrix is used as input to an integer programming model to obtain a strict total order that provides a transitive ranking for the set of alternatives. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 155–163, 2014     

军用数字地图中政区的构建及绘制方法

依据境界之间的拓扑数据,采用拓扑分析、边界追踪、边界闭环构建、边界约束下的凸分解、区域填充和边界符号化等技术手段,提出了OpenGL渲染环境下军用数字地图政区的构建方法.通过具体的软件开发和真实数据的测试,证明该方法生成政区准确、符号美观,可适用于不同比例尺下数字地图的显示.该算法具有较强的通用性,遵循国军标的相关规定,已经在相关数字地图软件中得以应用.     

Banach空间中拟非扩展映象的不动点的迭代逼近

研究了严格凸Banach空间中非空间凸子集上拟非扩展映象的不动点的迭代逼近问题,主要证明了:设E是严格凸Banach空间,K为E的闭凸子集,T:K→K为连续拟非扩展映象。进一步假设T(K)包含于K的一个紧子集之中,迭代地定义序列{xn}∞n=1如下:(IS)yn=(1-βn)xn+βnTxn,n≥1,xn+1=(1-αn)xn+αnTyn,n≥1,其中{αn}和{βn}满足一定的条件,则{xn}强收敛于T的某个不动点。     

Maximizing the ratio of two convex functions over a convex set

The purpose of this article is to present an algorithm for globally maximizing the ratio of two convex functions f and g over a convex set X. To our knowledge, this is the first algorithm to be proposed for globally solving this problem. The algorithm uses a branch and bound search to guarantee that a global optimal solution is found. While it does not require the functions f and g to be differentiable, it does require that subgradients of g can be calculated efficiently. The main computational effort of the algorithm involves solving a sequence of subproblems that can be solved by convex programming methods. When X is polyhedral, these subproblems can be solved by linear programming procedures. Because of these properties, the algorithm offers a potentially attractive means for globally maximizing ratios of convex functions over convex sets. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Minimizing sums and products of linear fractional functions over a polytope

In this paper, we develop efficient deterministic algorithms for globally minimizing the sum and the product of several linear fractional functions over a polytope. We will show that an elaborate implementation of an outer approximation algorithm applied to the master problem generated by a parametric transformation of the objective function serves as an efficient method for calculating global minima of these nonconvex minimization problems if the number of linear fractional terms in the objective function is less than four or five. It will be shown that the Charnes–Cooper transformation plays an essential role in solving these problems. Also a simple bounding technique using linear multiplicative programming techniques has remarkable effects on structured problems. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 583–596, 1999     

函数变换提高灰色预测模型精度的条件

指出选择函数变换来提高模型精度主要与三个方面的因素有关：提高数据序列的光滑比、调整数据序列的级比和确保凸凹性。在调整级比方面,扩充了级比压缩变换的相关定理,并讨论了几种常用的函数变换在上述三个方面的关系。最后结合实例提出,对于变换后的数据序列若不满足这三方面的要求可以再进行函数变换以达到提高模型精度的目的。     

复Banach空间的凸性及 Hp 鞅

本文系统地讨论了复Ｂａｎａｃｈ空间的各种凸性,以及取值于复Ｂａｎａｃｈ空间的Ｈｐ鞅,得到了关于凸性及Ｈｐ鞅之间的各种等价性命题。     

几何凸集中一个递归关系的建立与求解

几何凸集中递归关系的建立是求解问题的关键。本文对一个定理中递归关系的建立给出了容易理解的详细表述,然后利用生成函数法求其解。