退化问题中Bland规则的改进

Bland规则是退化问题中避免循环的一种方法，本给出了Bland规则的两种改进形式，并从理论上证明了规则Ⅲ为有限规则，另外，还对一个退化问题给出了相应于不同规则的解法。     

二流体系统中自由面及界面上的二阶椭圆余弦波*

本文考虑[1]中所建立的模式,采用约化摄动法及PLK方法,求得了自由面及界面上的二阶椭圆余弦波。在退化情况下与文[3]和[4]的结果符合。     

一类脉冲微分方程的光滑多尺度解

利用奇异摄动方法,提供了一种以光滑的多尺度解的观点来研究一类脉冲微分方程.通过引入适当的奇异摄动项,定义了相应的奇异摄动边值问题,其对应的退化方程即为原脉冲微分方程.利用边界层函数法和缝接法,构造了该奇异摄动边值问题的光滑多尺度解,并有效地刻画原脉冲微分方程的不连续解,同时也证明了多尺度解的存在性及余项估计.最后,通过实例,验证了文中的主要结果.     

指数二分性与自治奇摄动系统的退化同宿分支

利用指数二分性理论和泛函分析方法，我们研究了自治奇摄动系统的同，异宿轨道的存在性，给出了高维奇摄动系统从退化系统分支出同异宿轨道的Ｍｅｌ－ｎｉｋｏｖ型函数。     

二阶半线性奇摄动边值问题的渐近解

研究不满足法向双曲条件的二阶半线性非自治奇摄动Dirichlet边值问题.首先,利用边界层函数法,构造了问题在两个区间端点的代数边界层,获得了形式渐近解;接着,利用上下解方法,证明了解的存在性、渐近解的一致有效性以及渐近解与精确解之间的误差估计.研究表明:通过对奇异摄动参数进行适当的尺度变换,一定条件下可处理任意退化的二阶半线性非自治奇摄动边值问题.最后,通过一个典型例子验证了理论结果的正确性.     

关于奇异摄动问题数值解法的一个猜测的证明

在这篇文章中,我们就二阶常微分方程奇异摄动边值问题证明了Doolan,Miller和Schilders提出的一个猜测,即差分格式的一致收敛阶数不超过退化差分格式对退化问题的收敛阶数。对一般的线性奇异摄动问题,本文的证明方法都适用。     

一类具有高阶转向点的二次问题的奇摄动

研究带有高阶转向点的二阶非线性微分方程的边值问题εy″=f(t)y′2+g(t,y)y(a,ε)=A,y(b,ε)=B的奇异摄动现象.在一定的条件下,得到了摄动解关于退化解的渐近性质及误差估计.     

具有摄动边界薄膜振动Robin问题的可解性研究

研究了一个具有摄动边界薄膜振动的R ob in问题,利用参数变形法及问题的可解性条件,得到了该问题非退化的振动频率与振动模态.     

半导体技术中数学模型的渐近分析

本文在非平衡状态下，研究了具有Dirichlet边界条件的稳态半导体模型的解的渐近性态。首先，对N维半导体模型，结合解在L^∞和H^1空间一致有界性，论证了奇异摄动问题的解的极限满足相应的退化问题且在H^1中弱收敛。然后，对一维半导体模型，进一步证明了解在H^1中强收敛。     

Lamé函数和非线性演化方程的新多级准确解

基于Lamé方程和新的Lamé函数,应用摄动方法和Jacobi椭圆函数展开法求解非线性演化方程,获得多种新的多级准确解.这些解在极限条件下可以退化为各种形武的孤波解.     

A dual perturbation view of linear programming

Solving standard-form linear prograrns via perturbation of the primal objective function has received much attention recently. In this paper, we investigate a new perturbation scheme which obtains a dual optimal solution by perturbing the dual feasible domain under different norms. A dual-to-primal conversion formula is also provided. We show that this new perturbation scheme actually generalizes the primal entropic perturbation approach to linear programming.Partially sponsored by the North Carolina Supercomputing Center 1994 Cray Research Grant and the National Textile Center Research Grant.     

An unconstrained dual approach to solving Karmarkar-type linear programs using conventional barrier functions

This paper proposes an unconstrained dual approach and an efficient algorithm for solving Karmarkar-type linear programming problems. Conventional barrier functions are incorporated as a perturbation term in the derivation of the associated duality theory. An optimal solution of the original linear program can be obtained by solving a sequence of unconstrained concave programs, or be approximated by solving one such dual program with a sufficiently small perturbation parameter. A globally convergent curved-search algorithm with a quadratic rate of convergence is designed for this purpose. Based on our testing results, we find that the computational procedure is very efficient and can be a viable approach for solving linear programming problems.     

The multiparametric 0–1-integer linear programming problem: A unified approach

We designed an algorithm for the multiparametric 0–1-integer linear programming (ILP) problem with the perturbation of the constraint matrix, the objective function and the right-hand side vector simultaneously considered. Our algorithm works by choosing an appropriate finite sequence of non-parametric mixed integer linear programming (MILP) problems in order to obtain a complete multiparametrical analysis. The algorithm may be implemented by using any software capable of solving MILP problems.     

Determination and Correction of an Inconsistent System of Linear Inequalities

In this paper the problems to determine an inconsistent system of linear inequalities and to correct its right-hand side vector are solved by using the isometric plane method for linear programming. As an example, the suitable perturbation quantity of the perturbed inequalities of ill-conditioned linear equations is determined in the numerical experiments.     

Perturbation bounds for the linear least squares problem subject to linear inequality constraints

We study the effect on the solution to a linear least squares problem with linear inequality and equality constraints when the data defining the problem are perturbed. The existence and uniqueness of a solution are investigated. If the matrices involved have full rank, then a detailed bound is obtained by the duality theory for quadratic programming. Sufficient conditions are derived for an estimate of the perturbation in the solution to hold in terms of the largest perturbation in the data.     

Constraint augmentation in pseudo-singularly perturbed linear programs

In this paper we study a linear programming problem with a linear perturbation introduced through a parameter ε > 0. We identify and analyze an unusual asymptotic phenomenon in such a linear program. Namely, discontinuous limiting behavior of the optimal objective function value of such a linear program may occur even when the rank of the coefficient matrix of the constraints is unchanged by the perturbation. We show that, under mild conditions, this phenomenon is a result of the classical Slater constraint qualification being violated at the limit and propose an iterative, constraint augmentation approach for resolving this problem.     

Sensitivity analysis in linear semi-infinite programming: Perturbing cost and right-hand-side coefficients

This paper analyzes the effect on the optimal value of a given linear semi-infinite programming problem of the kind of perturbations which more frequently arise in practical applications: those which affect the objective function and the right-hand-side coefficients of the constraints. In particular, we give formulae which express the exact value of a perturbed problem as a linear function of the perturbation.     

Schwankungsbereiche linearer Optimierungsaufgaben

Summary A perturbation analysis of the linear programming problem is performed. Limits are given within which the coefficients may vary without disturbing a feasible basis or the optimal basis. A numerical example illustrates the techniques.     

PRIMAL PERTURBATION SIMPLEX ALGORITHMS FOR LINEAR PROGRAMMING

1. IntroductionExtensive research in linear programming, such as [1,2,9,10,if, 12,13,14,19], hasbeen to improve pivot rules to reduce the number of iterations required. Relatively lesseffort was made on perturbing problem data with pivot rules unaltered (for instance, theself--dual parametric method [7] and perturbation--based methods [3,5]). And, becauseof the papametrization, the latter do not proceed as simply as the conventional simplexalgorithm itself.Recently, Pan [17] proposes new pert…     

An extension of the entropic perturbation method of linear programming

In this paper, an extended form of the entropic perturbation method of linear programming is given, which can overcome the weakness of the original method - being easy of overflow in computing. Moreover, the global convergence of the gradient algorithm for the method is discussed.