一类求解分片延迟微分方程的线性多步法的散逸性

本文研究分片延迟微分方程本身及数值方法的散逸性问题．给出了一个关于此类问题本身散逸性的充分条件,同时得到了一类求解此类问题的线性多步法的数值散逸性结果,此结果表明所考虑的数值方法继承了方程本身的散逸性．数值试验进一步验证了理论结果的正确性．  

证券组合投资的多目标区间数线性规划模型

本文提出了证券组合投资的多目标区间数线性规划模型，引入了收益——风险偏好参数和优化水平参数。投资者可以根据对风险的喜好程度和金融市场的客观情况，适当估计这两个参数，从而得到相应情况下的有效投资方案，使投资过程更具柔性，而且更接近于实际情况。  

求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt算法

本文提出了求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt算法,即μk=ακ(θ||F_k|| (1-θ)||J_k~TF_k||),θ∈[0,1],其中ακ利用信赖域技巧来修正.在不必假设雅可比矩阵非奇异的局部误差界条件下,证明了该算法是全局收敛和局部二次收敛的.数值试验表明该算法能有效地求解奇异非线性方程组问题.  

An improved rounding method and semidefinite programming relaxation for graph partition

Given an undirected graph G=(V,E) with |V|=n and an integer k between 0 and n, the maximization graph partition (MAX-GP) problem is to determine a subset S⊂V of k nodes such that an objective function w(S) is maximized. The MAX-GP problem can be formulated as a binary quadratic program and it is NP-hard. Semidefinite programming (SDP) relaxations of such quadratic programs have been used to design approximation algorithms with guaranteed performance ratios for various MAX-GP problems. Based on several earlier results, we present an improved rounding method using an SDP relaxation, and establish improved approximation ratios for several MAX-GP problems, including Dense-Subgraph, Max-Cut, Max-Not-Cut, and Max-Vertex-Cover. Received: March 10, 2000 / Accepted: July 13, 2001?Published online February 14, 2002  

求解三维高次拉格朗日有限元方程的代数多重网格法

本文针对带有间断系数的三维椭圆问题，讨论任意四面体剖分下的二次拉格朗日有限元方程的代数多重网格法．通过分析线性和高次有限元空间之间的关系，我们给出了一种新的网格粗化算法和构造提升算子的代数途径．进一步，我们还对新的代数多重网格法给出了收敛性分析．数值实验表明这种代数多重网格法对求解二次拉格朗日有限元方程是健壮和有效的。  

A Conic Trust-Region Method for Nonlinearly Constrained Optimization

Trust-region methods are powerful optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. Can we combine their advantages to form a more powerful method for constrained optimization? In this paper we give a positive answer and present a conic trust-region algorithm for non-linearly constrained optimization problems. The trust-region subproblem of our method is to minimize a conic function subject to the linearized constraints and the trust region bound. The use of conic functions allows the model to interpolate function values and gradient values of the Lagrange function at both the current point and previous iterate point. Since conic functions are the extension of quadratic functions, they approximate general nonlinear functions better than quadratic functions. At the same time, the new algorithm possesses robust global properties. In this paper we establish the global convergence of the new algorithm under standard conditions.  

一类变换半群的秩

设自然数n≥4,X_n={1,2,…,n},证明了X_n上的保序压缩全变换半群W_n的秩为n-1.  

广义拉回与推出

利用逆向极限刻画集体拉回与I-拉回,探讨I-拉回与拉回间的关系;并把集体拉回和I-拉回统一起来,引入拉回的另一推广形式,即广义拉回,研究它在一般范畴及环、模范畴上的性质,应用到拉回环,得到拉回环上倾斜模间的关系及几类广义拉回环的同调维数的上界。  

一个解无约束优化问题的过滤信赖域方法

1 引言 本文中,我们考虑一般的无约束极小化问题: minx∈Rn f(x), (1.1) 其中f:Rn→R二次连续可微. 信赖域方法是解问题(1.1)的一类非常成功的算法.在标准信赖域算法框架([2][11][1])中,迭代点列是单调下降的,对于一些坏条件问题,会出现收敛非常缓慢的情形.针对这种问题,人们提出了非单调技术([2][3][13][14][15]),来加快算法在实际计算中的收敛速度,取得了很好的数值效果.  

Boundary blow-up solutions and their applications in quasilinear elliptic equations

Based on a comparison principle, we discuss the existence, uniqueness and asymptotic behaviour of various boundary blow-up solutions, for a class of quasilinear elliptic equations, which are then used to obtain a rather complete understanding of some quasilinear elliptic problems on a bounded domain or over the entireR ^N .