A NEW PERTURBATION SIMPLEX ALGORITHM FOR LINEAR PROGRAMMING

1.IntroductionThedualsimplexalgorithm[1,91andtheprimal-dualsimplealgorithm[6]arewellknownandefficientsimplexvariants.However,bothofthemneedaninitialdualfeasiblebasistogetstarted,andthereforecannotbedirectlyappliedtosolvingproblemsthatdonothavesuchane...     

一个求解线性规划的单纯形-内点算法

根据单纯形方法和大步长路径跟踪算法（Ｈｅｒｔｏｇ，Ｒｏｏｓ和Ｔｅｒｌａｋｙ１９９１），对于具有不等式约束的线性规划问题，引进了一个具有组合特性的内点算法．该方法保留了单纯形方法和内点算法的优点，克服了它们的不足，在任何情况下，这个方法都能快速收敛．数值结果也很好地验证了这个结论．     

变量有广义界线性规划的叠累单纯形法

本文建立变量有广义界线性规划一个新的转轴算法,称之为叠累单纯形算法,新算法其有三个主要特征：１对于检验数为“坏”的非基变量 ｘｓ,进行一轮子转轴运算,使得ｘｓ进基,转轴中具有“好”的检验数的变量始终保持“好”的检验数;２ｘ．进基的子转轴所产生的基既不是原始可行基,也不是对偶可行基,但子转轴结束时产生的基是原始可行的;３目标函数值在整个转抽运算中是单调下降,从而算法可有限步终止．     

A FAST SIMPLEX ALGORITHM FOR LINEAR PROGRAMMING

Recently, computational results demonstrated remarkable superiority of a so-called ＂largest-distance＂ rule and ＂nested pricing＂ rule to other major rules commonly used in practice, such as Dantzig＇s original rule, the steepest-edge rule and Devex rule. Our computational experiments show that the simplex algorithm using a combination of these rules turned out to be even more efficient.     

MOORE-PENROSE INVERSE SIMPLEX ALGORITHMS BASED ON SUCCESSIVE LINEAR SUBPROGRAMMING APPROACH

Generalized simplex variants based on successive linear subprogramming approach (SLS) are described in this paper. In stead of inverse matrix, these variants employ Moore-Penrose inverse. They are respectively characterized by different pivoting rules, Numerical results of limited tests show encouraging performance of these variants.     

线性规划的最钝角CRISS-CROSS算法

1 引言 考虑如下标准线性规划问题 minimize c~Tx (1) subject to Ax=b, x≥0 其中A∈R~(m×n) (m相似文献   

线性规划的单纯形法及其发展

本文给出了一种新的原对偶单纯形法,并通过它分析了隐藏在经典单纯形法中的对偶信息．我们重新评价经典单纯形法并详细讨论了它与现代单纯形法之间的联系．两个修改版本一并给出．新算法具有计算量小和实施简单等特点,计算效果也不错．初步数值实验表明现代单纯形法比经典方法具有明显的优越性．     

线性规划初始基可行解的一种直接算法

本文通过引入可变动目标函数的预规划来求线性的初始基可行解，可以大量减少外额变量的个数，从而简化了二阶段单纯形法，使之便于在计算机上实现。     

线性规划的对偶基线算法

In this paper,we studied the dual form of the basic line algorthm for linear programs.It can be easily implemented in tableau that similar to the primal/dual simplex method.Different from primal simplex method or dual simplex method,the dual basic line algorithm can keep primal feasibility and dual feasibility at the same time in a tableau,which makes it more efficient than the former ones.Principles and convergence of dual basic line algorthm were discussed.Some examplex and computational experience were given to illustrate the efficiency of our method.     

线性规划流动等值面算法

对于线性规划问题,本文给出了基于流动等值面的等价模型,提出了一种不可行流动等值面算法．新算法保留了传统单纯形算法的优点并克服了它的不足。初步数值结果表明新算法比传统方法更为有效．     

EXPECTED NUMBER OF ITERATIONS OF INTERIOR-POINT ALGORITHMS FOR LINEAR PROGRAMMING

We study the behavior of some polynomial interior-point algorithms for solving random linear programming (LP) problems. We show that the expected and anticipated number of iterations of theseTodd‘s probabilisticalgorithms is bounded above by O(n^1.5). The random LP problem is model with the Cauchy distribution.     

一种改进的多维偏好线性规划分析方法

本文对传统的多维偏好线性规划分析方法—LINMAP法进行改进,提出一种新的多维偏好线性规划分析方法,该方法运用加性加权法建立线性规划模型,同时引入任意小正数δ,使得评价结果更加符合决策人偏好集。     

多层线性规划问题的整体优化算法

本文研究了求解多层线性规划问题的整体优化算法,利用流动等值面技术,证明了算法的有限终止性,并给出实际例子验证了算法的有效性.     

解半定规划的二次摄动方法

半定规划在系统论,控制论,组合优化,和特征值优化等领域有着广泛的应用。本文将半定规划摄动成二次半定规划,它的唯一解恰为原问题的解,并且对其偶问题等价于一个线性对称的投影方程,可方便地用投影收缩方法求解,从而获得原半定规划问题的解。文章给出了算法及其收敛性分析,数值试验结果表明摄动方法是解半定规划的一种有效的方法。     

CALCULATION OF PENALTIES IN ALGORITHM OF MIXED INTEGER PROGRAMMING SOLVING WITH REVISED DUAL SIMPLEX METHOD FOR BOUNDED VARIABLES

1.IntroductionThestudiesonthebranch--and--boundalgorithmofintegerprogramminghavebeencarriedoutsince60's.TheeffortsinimprovingthealgorithmaremainlyconcentratedonspeedinguptherelatedLPsolutionforeachnodeandmakingbetterselectionofnodeandbranchforexaming...     

ABS ALGORITHMS FOR SOLVING LINEAR INEQUALITIES

We consider a class of ABS type algorithms for solving system of linear inequalities, where the number of inequalities does not exceed the number of variables.     

A SCALED CENTRAL PATH FOR LINEAR PROGRAMMING

1. IntroductionIllterior poillt methods are one of the most illtensively studied topics in optinistion. Thousands of publications have been appeared on inferior point ndhods. A very good recent reviewis given by [4]. Interior point methods have very good theoretical properties including thenice polynomial complexity prOPerty. And more haportat is that numerous applications haveshown that interior point methods are very efficient for solving large sparse linear progr~ngproblemS. Interior poil…     

一个改进的线性规划预校正算法

本文我们提出了一个改进型线性规划预校正算法，我们的预步和校正步方向与Mizuno－Todd-Ye[4]的方向是不同的．我们的算法的迭代复杂度为，然而在校正步，我们降低对偶间隙一个常数因子．     

整数线性规划的一种新的割平面法

本文提出了一种新的求解整数线性规划的割平面思路 .它利用目标函数等值面的移动来切割与(IL P)相应的 (SL P)可行域的“无用”部分 ,再通过扩大与 (SL P)最优基相应的非基变量的取值来压缩 (SL P)的可行域 ,由此求得整数线性规划的最优解 .     

DEGENERATE OPTIMAL BASIS GRAPHS IN LINEAR PROGRAMMING

§ 1　IntroductionA graph-theoretic approach for investigating basis transformations in a linear pro-gramming has been historically developed.Let V be the setof all bases with respectto thecolumn vectors of a matrix A.Two bases are called adjacentifthey can be transformed intoeach other by a pivot operation.Denote by E the set of edges each of which is incidentwith a pair of adjacentbases.Then G=(V,E) is called the basisgraph of matrix A(or ofthe corresponding LP) .Tucker[1 ] first called…