第一阶段原有单纯形和对偶单纯形算法的计算比较

线性最优化广泛应用于经济与管理的各个领域.在线性规划问题的求解中,如果一个初始基本可行解没有直接给出,则常采用经典的两阶段法求解.对含有"≥"不等式约束的线性规划问题,讨论了第一阶段原有单纯形法和对偶单纯形法两种算法形式,并根据第一阶段问题的特点提出了改进的对偶单纯形枢轴准则.最后,通过大规模数值试验对两种算法进行计算比较,结果表明,改进后的对偶单纯形算法在计算效率上明显优于原有单纯形算法.     

对于单纯形法矩阵描述的认识

从修正单纯形法的提出、对偶单纯形法的出现、对偶问题最优解的确定以及灵敏度分析的基本依据等四个方面阐述了对单纯形法矩阵描述的认识,充分显示出单纯形法矩阵描述在线性规划发展中的重要性.     

双层线性规划的一个全局优化方法

用线性规划对偶理论分析了双层线性规划的最优解与下层问题的对偶问题可行域上极点之间的关系，通过求得下层问题的对偶问题可行域上的极点，将双层线性规划转化为有限个线性规划问题，从而用线性规划方法求得问题的全局最优解．由于下层对偶问题可行域上只有有限个极点，所以方法具有全局收敛性．     

广告媒体最佳选择的定量分析

本文应用线性规划问题的对偶单纯形法，分析广告媒体选择问题的最佳组合     

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   

线性规划对偶单纯形法的常识性经济解释

线性规划对偶单纯形法的数学描述是抽象且不易理解的 ,本文找到了一种常识性经济解释的描述 .既通俗易懂、又能抓住方法的实质 .这将从通俗易懂的思想方法上促进线性规划问题解法的普及推广应用     

关于多目标线性规划单纯形法中寻找对偶解的讨论

本文我们讨论当用单纯形法得到一个多目标线性规划问题的有效解或弱有效解时,寻找对偶解的条件。     

线性规划单纯形法主元规则的几何分析

本文研究了线性规划单纯形法和对偶单纯形法主元规则的性质.利用直观的几何方法,结合对偶理论和灵敏度分析,得到了主元规则的特点,针对针对三种最常见的主元规则构造出不同的二维和三维例子,以此说明对每种主元规则都容易构造出其不优的反例,以及迭代次数多于约束个数的例子.所得结果有助于对单纯形法和对偶单纯形法的理解和研究.     

线性规划可行解的一个性质

通过对线性规划问题可行解的性质的推广,导出推广后的可行解与对应的对偶线性规划的约束条件之间互为充分必要的关系。     

一种用于线性规划算法的换基准则

本文就线性规划中的对偶单纯形法和运输问题中的表上作业法选取出基变量或者对基变量的准则进行改进,从而得出一种新的换基准则.按该方法进行优化运算,可以使算法的迭代次数减到最少,从而加快了运算速度.     

互补基解性质的应用研究

对线性规划互补基解性质进行了研究,得到了由线性规划问题最优基对应的单纯形表直接获得对偶线性规划问题最优基对应的单纯形表的一个有效方法,给出了应用实例.     

关于线性规划问题熵障碍对偶法的注记

线性规划是目标优化问题中最常用的模型。关于大规模线性规划问题的有效求解问题一直受到人们的关注。熵障碍对偶法是继内点法之后,又一解线性规划问题的新的算法。本文讨论了熵障碍对偶法的推广形式及其梯度类算法的收敛性。     

Using dual network bounds in algorithms for solving generalized set packing partitioning problems

This article deals with a method to compute bounds in algorithms for solving the generalized set packing/partitioning problems. The problems under investigation can be solved by the branch and bound method. Linear bounds computed by the simplex method are usually used. It is well known that this method breaks down on some occasions because the corresponding linear programming problems are degenerate. However, it is possible to use the dual (Lagrange) bounds instead of the linear bounds. A partial realization of this approach is described that uses a network relaxation of the initial problem. The possibilities for using the dual network bounds in the approximation techniques to solve the problems under investigation are described.     

Understanding linear semi-infinite programming via linear programming over cones

In this article, the standard primal and dual linear semi-infinite programming (DLSIP) problems are reformulated as linear programming (LP) problems over cones. Therefore, the dual formulation via the minimal cone approach, which results in zero duality gap for the primal–dual pair for LP problems over cones, can be applied to linear semi-infinite programming (LSIP) problems. Results on the geometry of the set of the feasible solutions for the primal LSIP problem and the optimality criteria for the DLSIP problem are also discussed.     

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.     

Sign consistent linear programming problems

This article studies linear programming problems in which all minors of maximal order of the coefficient matrix have the same sign. We analyse the relationship between a special structure of the non-degenerate dual feasible bases of a linear programming problem and the structure of its associated matrix. In the particular case in which the matrix has all minors of each order k with the same strict sign ? _k , we provide a dual simplex revised method with good stability properties. In particular, this method can be applied to the totally positive linear programming problems, of great interest in many applications.     

线性规划无穷多最优解的讨论

利用线性规划单纯形表对线性规划原问题存在无穷多最优解和对偶问题存在无穷多最优解的情况进行了讨论,并分析了对偶问题存在无穷多最优解情况下的影子价格的方向性。最后以实例说明了各种情况。对初学者加深理解及决策者决策参考有一定帮助     

Eliminating columns in the simplex method for linear programming

We propose a column-eliminating technique for the simplex method of linear programming. A pricing criterion is developed for checking whether a dual hyperplane corresponding to a column intersects a simplex containing all of the optimal dual feasible solutions. If the dual hyperplane has no intersection with this simplex, we can eliminate the corresponding column from further computation during the course of the simplex method.The author is grateful for many discussions with Professor G. B. Dantzig, Stanford University, and for his valuable suggestions about this work. The author also gratefully acknowledges the editor and two referees for their very helpful comments, corrections, and remarks.