COMPUTATIONAL COMPLEXITY OF INTEGRATION AND DIFFERENTIATION OF CONVEX FUNCTIONS

In this paper,we study the computational complexity of the integrals and the derivatives ofconvex functions defined on the interval [0,1].     

关于凸函数的一个不等式

一、引言 设M(x)是[0, ∞)上的凸单调增函数,f(x)是[0,a]上的非负有界变差函数,且M(0)=f(0)=0。 本文给出不等式V_0~a[M(f(x))]≤M(V_0~a[f(x)]),(1) 其中V_0~a[f(x)]表示函数f(x)在[0,a]内的全变差。作为一个应用,我们还将由此导出Opial-华氏不等式的一个推广。     

非线性规划中的梯度投影方法

这是一篇对非线性规划中梯度投影法的综述。通过对以前工作的讨论,我们为今后的研究提出几个有趣的问题。     

OPTIMAL ASSEMBLY BY MONOTONIC PROPERTY

Consider a system containing a type of n devices.Each device consists of mparts.Given mn parts for n devices with different working probabilities,how do we groupthem into n devices such that the system is most reliable.A monotonic grouping means thatthe best parts are put together,then the best remaining parts are put together,etc..Asufficient and necessary condition for such grouping being optimal will be given in thispaper.As an application,we show that the monotonic grouping is optimal for the two-stagek-out-of-n system.When m=2,we also study the grouping that the best pairs to the worst,the second best pairs to the second worst,etc.,associated with a redundant device problem.     

关于等价中介殆周期函数和Dohr殆周期函数

当且仅当Bohr殆周期是殆周期时,Hausdorff群中的连续复值函数是一个Bohr殆周期函数。     

阀门布局问题的一个最优性判别条件

给定非空点集x及其n对非空子集x_i,y_i,x_i∩y_i=φ(i=1,2,…,n)。找出一个图G,满足条件(a)V(G)=x;(b)对i=1,2,…,n,G皆有连通子图G_i,使x_i(?)V(G_i)和y_i∩V(G_i)=φ,且使|E(G)|最小。本文指出上述问题的一个最优性判别条件;并利用Hall定理及若干引理给出严格的数学证明。     

ON A NEW GRADIENT PROJECTION METHOD

In 1983,Du and Sun gave an algorithm which possesses superiorities of both Rosen'sgradient projection method and Wolfe's reduced gradient method.However,in order to have theprovable global convergence,the algorithm includes an ε-procedure as one of its parts.In this paper,we delete such a part and prove a convergence theorem.     

Roser-Polak算法的改进

一、引言 为了改善Rosen方法的收敛性,Polak引入了ε程序,并在所谓ε假设下,证明了修改后的Rosen-Polk算法的收敛性。章祥荪进一步证明了ε假设和正则性假设的等价性。本     

计算复杂性理论的近况与展望

本文是有关计算复杂性方面的综述,笔者参加了1985年到1986年间在美国加里福尼亚大学举行的有关这一理论方面的几次学术会议,就从这活动中得到的信息作一详细介绍,同时谈一些自己的看法。     

图可重构的充要条件

众所周知,Ulam在1929年提出了重构猜想,后来收集在文献[1]中、在文献[2]中,Bondy等人列出了一系列尚未解决的问题,重构猜想位居第一。Kelly证明了重构猜想对树是