THE EIGENVALUE PERTURBATION BOUND FOR ARBITRARY MATRICES

In this paper we present some new absolute and relative perturbation bounds for theeigenvalue for arbitrary matrices, which improves some recent results. The eigenvalueinclusion region is also discussed.     

Worm Problem的一个新上界

1966年,Leo Moser提出了一个基本的几何问题,即Worm Problem．该问题是指:在平面上寻找一个面积最小的(凸)区域,使得任何一条长为1的平面曲线都能够通过旋转和平移完全放入该(凸)区域之中．对于要寻找的区域是凸的情形,本文将把目前所知道的最小的上界由0．2738086降低至0．270911861．在最后一部分,我们推广了Worm Problem,并初步给出了一些相应的结果．     

一个带有线搜索的新信赖域方法及其收敛性

本文利用一个修正的BFGS公式,提出了一个结合Armijo线搜索条件技术的BFGS信赖域方法,并在一定条件下证明了该方法的全局收敛性和超线性收敛性.初步的数值实验结果表明该方法是有效的.     

A new trust region technique for the maximum weight clique problem

A new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of other stationary points of the program. We formulate and prove a condition when a Motzkin-Straus optimum coincides with such a point. The developed method has complexity O(n³), where n is the number of vertices of the graph. It was implemented in a publicly available software package QUALEX-MS.Computational experiments indicate that the algorithm is exact on small graphs and very efficient on the DIMACS benchmark graphs and various random maximum weight clique problem instances.     

Empirical likelihood for AR-ARCH models based on LAD estimation

By employing the empirical likelihood method,confidence regions for the stationary AR(p)-ARCH(q) models are constructed.A self-weighted LAD estimator is proposed under weak moment conditions.An empirical log-likelihood ratio statistic is derived and its asymptotic distribution is obtained.Simulation studies show that the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy,especially for relative small size of observation.     

Objective Function Features Providing Barriers to Rapid Global Optimization

The purposes of this discussion paper are twofold. First, features of an objective function landscape which provide barriers to rapid finding of the global optimum are described. Second, stochastic algorithms are discussed and their performance examined, both theoretically and computationally, as the features change. The paper lays a foundation for the later findings paper.     

On the zeros of functions in Bergman spaces and in some other related classes of functions

A well-known theorem of H.S. Shapiro and A.L. Shields implies that if f?0 is a function which belongs to the Bergman space Ap (0<p<∞) and {zk} is a sequence of zeros of f which is contained in a Stolz angle, then {zk} satisfies the Blaschke condition. In this paper we improve this result. We consider a large class of regions contained in the unit disc D which touch ∂D at a point ξ tangentially and we prove that the mentioned result remains true if we substitute a Stolz angle by any of these regions of tangential approach.     

THE POINCAR BIFURCATION OF QUADRATIC SYSTEMS HAVING A REGION CONSISTING OF PERIODIC CYCLES BOUNDED BY A HYPERBOLA AND AN ARC OF EQUATOR

The usual bifureation problems oeeurred in the study of the Planar differential systems having a region eonsisting of Periodie eycles are as follows:15 there any closed orbit whieh generates limit eyeles after a small perturbation?How many limit eyel