弧搜索内点算法

利用弧搜索内点算法对线性规划问题进行求解,得到该算法的多项式复杂度为O(n3/4 L).该算法在中心路径的一个宽邻域内,沿椭圆近似寻找线性规划的最优解.数值实验表明了该算法的有效性.

数值最优化的弧搜索方法

非线性最优化算法主要包括两个步骤:一是利用目标函数和约束函数的导数或相关信息来确定搜索方向,二是利用一维搜索和信赖域方法来确定沿搜索方向步长.一维直线搜索在各种教科书及参考文献中被广泛地讨论过,而另一种搜索方法弧搜索方法,在某些情况下更有效却鲜为人知.本文讨论弧搜索方法的一些细节及在各种最优化问题中的应用,并指出弧搜索技术比直线搜索对某些问题更具优越性.

一个不等式约束问题的SQP方法及其收敛性

提出一个关于不等式约束问题的SQP算法,其效益函数为非可微精确罚函数,罚因子具有自动调节性.通过求解一辅助线性方程组,获得二阶修正步,并利用弧式搜索,建立了问题的一个可行下降算法.在一定的假设条件下,证明了算法是全局收敛的,并且具有超线性收敛速度.

Implementation and comparative testing of turn-based algorithm for logit network loading

In order to evaluate the practicality and effectiveness of the turn-based algorithm for logit loading （TALL）, the TALL is implemented using C＋＋, and it is compared with a combination of the network-expanding method and the Dial algorithm based on the analysis of algorithm procedures. The TALL uses the arc-labeling shortest path searching, bidirectional star and the deque structure to directly assign the traffic flow, while the Dial algorithm should be used in an expanded network. The test results over realistic networks of eight cities show the superior performance of the TALL algorithm over the combination of the network-expanding method and the Dial algorithm, and the average processing time is reduced by 55. 4%. Furthermore, it is found that the operational efficiency of the TALL relates to the original densities of the cities. The average processing time is reduced by 65. 1% when the original density is about 14%, but the advantage of the TALL is not obvious with the increase in the original density.

Delaunay三角网生长法的一种改进方法

为了提高Delaunay三角网的构建速度,本文对三角网生长法进行了改进,提出了一种基于生长法的"弧带搜索排除"方法,通过一系列的圆弧将离散点区域划分成几个弧带,构网时,规定只可在当前弧带搜索第三点,该弧带离散点搜索完毕后进入下一弧带,如此循环。采用VC++6.0加以实现。测试表明,该方法能够加快构网速度,生成的三角形形状良好,具有一定的实际效用。