垂直线性互补问题的一步全局线性和局部二次收敛光滑Newton法

基于凝聚函数,提出一个求解垂直线性互补问题的光滑Newton法.该算法具有以下优点:(i)每次迭代仅需解一个线性系统和实施一次线性搜索;(ⅱ)算法对垂直分块P0矩阵的线性互补问题有定义且迭代序列的每个聚点都是它的解.而且,对垂直分块P₀+R₀矩阵的线性互补问题,算法产生的迭代序列有界且其任一聚点都是它的解;(ⅲ)在无严格互补条件下证得算法即具有全局线性收敛性又具有局部二次收敛性.许多已存在的求解此问题的光滑Newton法都不具有性质(ⅲ).     

Cascading failures in congested complex networks with feedback

In this article, we investigate cascading failures in complex networks by introducing a feedback. To characterize the effect of the feedback, we define a procedure that involves a self-organization of trip distribution during the process of cascading failures. For this purpose, user equilibrium with variable demand is used as an alternative way to determine the traffic flow pattern throughout the network. Under the attack, cost function dynamics are introduced to discuss edge overload in complex networks, where each edge is assigned a finite capacity (controlled by parameter α). We find that scale-free networks without considering the effect of the feedback are expected to be very sensitive to α as compared with random networks, while this situation is largely improved after introducing the feedback.     

A GENERALIZED GRADIENT PROJECTION METHOD FOR OPTIMIZATION PROBLEMS WITH EQUALITY AND INEQUALITY CONSTRAINTS ABOUT ARBITRARY INITIAL POINT

ＧＡＯＺＩＹＯＵ（高自友）（ＮｏｒｔｈｅｒｎＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１０００４４，Ｃｈｉｎａ）ＬＡＩＹＡＮＬＩＡＮ（赖炎连）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏ...     

非线性约束条件下的梯度投影—可行方向法

§1 引言对于约束条件为非线性的算法而言,具有收敛性的算法是不多的(参见[9])。1971年在[3]中,E.Polak提出了一个关于非线性约束的梯度投影-可行方向法,并证明了收敛性。1981年,章祥荪在[6]中又对E.Polak方法进行了改进。1985年堵丁柱在[7]工中对特定的非精确线搜索给出了一种具有收敛性的关于非线性约束的梯度投影-可行方向法。这些方法较以前那种先对切面做梯度投影,然后再拉回到可行域的传统梯度投影法(参见[2])具有了     

一个退化情况下非线性约束条件下的可行方向法

对于问题(P)∶{minf(x)|h_j(x)≤0,j=1,2,…,m;x∈E~n},Zoutendijk 在1960年提出了一个著名的可行方向法,但此算法不能保证所产生的点列是收敛的.1967年,Topkis 和 Veinott 通过对上述算法的修正,从而可以保证算法收敛到 Fritz-John点.但不能保证算法收敛到 Kuhn-Tucker 点.只有在非退化(即要求任可行点处     

提高道路交通系统的驾驶安全

道路交通系统是一个复杂的系统，其中包含了人的直接参与。在该系统中，人的因素起了重要的作用。本文中，在道路系统路面的某一点设计了一种类型控制信号，该点被称为信号点。在控制信号的作用下，当车辆经过信号点的时候，车辆需要降低速度。其目的在于能够通过控制信号控制交通流的状态，使其由无序变为有序，从而提高道路系统的交通安全。应用双车道的确定性NaSch模型进行仿真模拟，结果表明不仅交通流的状态能够由无序变为有序，而且交通流的状态是安全的。     

AN EFFECTIVE SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM FOR NONLINEAR OPTIMIZATION PROBLEMS

In this paper,a new globally convergent algorithm for nonlinear optimization prablems with equality and inequality constraints is presented. The new algorithm is of SQP type which determines a search direction by solving a quadratic programming subproblem per itera-tion. Some revisions on the quadratic programming subproblem have been made in such a way that the associated constraint region is nonempty for each point x generated by the algorithm, i. e. , the subproblems always have optimal solutions. The new algorithm has two important properties. The computation of revision parameter for guaranteeing the consistency of quadratic sub-problem and the computation of the second order correction step for superlinear convergence use the same inverse of a matrix per iteration, so the computation amount of the new algorithm will not be increased much more than other SQP type algorithms; Another is that the new algorithm can give automatically a feasible point as a starting point for the quadratic subproblems pe     

A new car-following model considering velocity anticipation

The full velocity difference model proposed by Jiang et al. [2001 Phys. Rev. E 64 017101] has been improved by introducing velocity anticipation. Velocity anticipation means the follower estimates the future velocity of the leader. The stability condition of the new model is obtained by using the linear stability theory. Theoretical results show that the stability region increases when we increase the anticipation time interval. The mKdV equation is derived to describe the kink--antikink soliton wave and obtain the coexisting stability line. The delay time of car motion and kinematic wave speed at jam density are obtained in this model. Numerical simulations exhibit that when we increase the anticipation time interval enough, the new model could avoid accidents under urgent braking cases. Also, the traffic jam could be suppressed by considering the anticipation velocity. All results demonstrate that this model is an improvement on the full velocity difference model.     

固定闭塞系统中列车流的特性分析

在NS模型的基础上，针对轨道交通的特点，本文提出一种用于模拟四显示固定闭塞系统的元胞自动机模型.应用该模型模拟四显示固定闭塞系统中的列车延迟的交通现象，分析了四显示固定闭塞系统中的发车时间间隔、客货车比例、车站停靠时间、停靠站台数量等因素对列车平均延迟时间的影响.结果表明：客、货车混行时，货车对后行客车的运行会产生抑制作用，调整客、货车在车站的停靠时间可有效缓解这种抑制作用，减少客车的延迟时间；增加停靠站台的数量可提高线路上的车流密度，缓解车流延误，但在较大的发车时间间隔时，站台的利用率会降低. 关键词： 元胞自动机 固定自动闭塞系统 列车延迟     

非线性约束条件下的SQP可行方法

本文对非线性规划问题给出了一个具有一步超线性收敛速度的可行方法。由于此算法每步迭代均在可行域内进行，并且每步迭代只需计算一个二次子规划和一个逆矩阵，因而算法具有较好的实用价值。本文还在较弱的条件下证明了算法的全局收敛和一步超线性收敛性。