查询词典 regularly convex function

A class of modified BFGS algorithm which satisfies the new quasi-Newton equation is proposed in the paper[1],and the global convergence of the algorithm is proved under the condition that the objective function is uniformly convex.

文献[1]曾在已建立的一类新拟牛顿方程 Bk+1sk=yk-=yk+kγskTsksk的基础上，证明了满足新拟牛顿方程的一类改进BFGS算法在目标函数为一致凸的条件下，具有全局收敛性。

In this paper,several quasi-Newton algorithms are generalized to a class of new quasi-Newton equation,several modified quasi-Newton algorithm s are obtained and their global convergence are proved under the objective function is uniformly convex.

将几个拟牛顿算法推广到一类新拟牛顿方程，得到几个修正拟牛顿算法；在目标函数为一致凸的条件下，证明了它们都具有全局收敛性。

The optimal model of indirected cost allocation for maximizing profit of enterprises using cost based pricing has been developed.The object function of maximizing profit has been shown convex.Then,a method of optimal indirected cost allocation for maximizing profit has been proposed.

在此基础上建立了企业在采用成本定价法时，以获得最大利润为目标的间接固定成本分摊的优化模型，证明了成本分摊的利润性能函数是一个凹函数，由此给出了一种利润最大化的间接固定成本的优化分配方法

Based on the idea and technical in the references[16],[17]and[26]as well as the theories of martingale,Brownian motion and stochastical orders,the expectation of present value of annuities with controlled random interests is obtained,and the upper bounds of present value function of discrete stochastic annuities with random interests in sense of convex order are derived,and the numerical characteristics of upper bounds are also obtained,furthermore,the expec

基于文[16]，[17]和[26]的思想方法以及鞅、反射Brownian运动和随机序的理论，得到了控制随机利率下连续年金现值的期望，并给出了离散随机年金现值函数在凸序意义下的上界，讨论了上界的分布函数和停止损失保费，进而得到了离散的随机年金现值的期望。

In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.

在巴拿赫空间理论中，Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一，分隔性定理是Hahn-Banach定理的重要应用，本文利用&超平面&的方法，改进了一个分隔性定理的证明；另外，本文利用邻域的&平移&方法，给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。

Winth the segmentation function, the stepwise decomposition algorithm can be used to compute the intersecting body volume not only of the convex polyhedrons, but also the concave polyhedrons.

像上面所讲到的多面体相交的体积计算这样一类问题，在其他行业也有类似问题的提出和反映，是值得认真研究和需要解决的问题。

Firstly, a new quasi convex-concave extension definition is introduced to study general constrained optimization problem, which is much approximate function's shape than the interval extension.

首先，对一般约束优化问题，引入一新的概念，即拟凸-凹扩张，它比区间扩张能更好地逼近函数的形状。

In chapter 7, quality loss cost is first used in the model of simultaneous design of tolerance, and economically attainable accuracy of position is first considered as constraint condition. It is first proven that the function of simultaneous design of tolerance is non-convex program; discrete and continuos Simulated Annealing are introduced; the optimum software to solve this model is given.

第七章首次将质量损失成本用于公差并行设计的优化数学模型中，并首次考虑位置精度的经济加工精度范围作为约束条件；论证了公差并行设计优化模型的非凸规划问题；着重介绍了离散型和连续型的模拟退火算法SA；研制了公差并行设计的优化软件。

In the fourth part, we study the growth velocity of q-mean square function of trigonometric martingales, using these we characterize TP q-uniformly convex of the space.

第四部分研究了q均方函数的增长速度与q一致TP可凸性的关系，从而用它们刻划了Banach空间的q一致TP可凸性。

In the third part,we study the growth velocity of q-mean square function of martingales , using these we characterize q-uniformly TC convex Banach space.

第三部分研究了q均方函数的增长速度与q一致TC可凸性的关系，从而用它们刻划了Banach空间的q一致TC可凸性。

Molecular Distillation is a kind of high vacuum distillation method, which is suitable for the separation of high boiling, heat sensitivity and viscidity products.

分子蒸馏技术是一种在高真空条件下进行的连续蒸馏过程，适合于分离高沸点、热敏性及具有生物活性的混合物。

They are to the Noughties what yuppies were to the Eighties .

那在六十年代是时髦的，但在八十年代肯定是过时了