Properties of the Central Points in Linear Programming Problems

In this paper we list several useful properties of central points in linear programming problems. We study the logarithmic barrier function, the analytic center and the central path, relating the proximity measures and scaled Euclidean distances defined for the primal and primal–dual problems. We study the Newton centering steps, and show how large the short steps used in path following algorithms can actually be, and what variation can be ensured for the barrier function in each iteration of such methods. We relate the primal and primal–dual Newton centering steps and propose a primal-only path following algorithm for linear programming.     

线性规划在回归分析中的应用

线性回归中,针对最小二乘法的两个替代准则一绝对离差和最小准则以及最大绝对离差最小准则,利用线性规划技术建立回归预测模型。实用分析表明,线性规划模型具有较好的预测效果,有郊地消除了统计数据中异常值对回归方程的影响。     

线性交叉规划的等价形式

本文利用参数规划的逆问题考虑交叉规划与多目标规划的关系,把交叉规划转变为部分同变量规划组,再把部分同变量规划组转化为一个多目标规划,并说明了交叉规划的均衡解与多目标规划的最优解的关系．     

On the Curvature of the Central Path of Linear Programming Theory

We prove a linear bound on the average total curvature of the central path of linear programming theory in terms of the number of independent variables of the primal problem, and independent of the number of constraints.     

The Concept of Proper Solution in Linear Programming

In this paper, we study the optimal solutions of a dual pair of linear programming problems that correspond to the proper equilibria of their associated matrix game. We give conditions ensuring the existence of such solutions, show that they are especially robust under perturbation of right-hand-side terms, and describe a procedure to obtain them.     

The Computation of Shadow Prices in Linear Programming

The purpose of this paper is to demonstrate that when degeneracy is present in an optimal basic solution to a linear programming problem, the optimal values of the dual variables do not necessarily correspond to shadow prices. In such instances, major commercial L.P. packages (such as IBM's MPS and MPSX) may provide misleading information about the shadow prices. It will be shown how the actual values of the shadow prices may be determined, and the nature of the relationship between shadow prices and dual variables will be discussed.     

基金最佳使用计划的线性规划模型

给出了基金存款策略的线性规划模型 .对基金 M使用 n年的情形 ,只需比较银行存款税后年利率 ,初步确定 n年内的一切可能有的基金存款方式及其到期本利率 ,通过基金流转分析 ,即可建立以最大奖金数为目标的线性规划模型 ( LP1 ) n;问题二则需先分析 n年内一切可行的存款和购国库卷的组合方式及其到期的最佳本利率 ,然后调整模型 ( LP1 ) .中有关的系数 ,即可得到模型 ( LP2 ) n,调整模型 ( LP1 ) n与 ( LP2 ) n中第三年的奖金 y的系数 ,即可得到问题三的线性规划模型 .本文用 SAS/OR软件求解上述模型 ,得到在 n=1 0 ,M=5 0 0 0的情形下 ,使每年奖金数为最大的各种问题的基金的最佳使用策略 .     

一般线性规划问题的限制逆问题

本文提出了一般线性规划问题的限制逆问题,利用线性规划的最优性条件,分别给出了其在l∞,l1,l2模意义下的数学模型,它们分别为线性规划和二次规划问题。     

Multiple Linear Curve Fitting

A technique for fitting a linear expression to data with errorsin all or any of the variables is described. The form of theerrors is restricted to the product of a row (data set) anda column (variable) error value. This form covers many practicalcases and allows the development of an efficient algorithm.     

求解多层线性规划的模糊规划法

本文用模糊集理论中的隶属函数描述多层线性规划的各层目标,在第一层给定最小满意水平下,通过求解相应层次的模糊规划来确定各层的最小满意度,从而最终得到问题的一个满意解。提出的方法只需求解一系列线性规划问题,具有较好的计算复杂性和可行性,最后的算例进一步验证了方法的有效性。     

Linear Programming on Microcomputers

The paper considers the problems involved in implementing linear programming software on microcomputers and the user requirements for packages on such machines.     

Introduction to Linear Programming

Journal of the Operational Research Society -     

线性约束凸规划的鞍梯度法

求线性约束凸规划问题的最优解。方法：在鞍梯度法的基础上提出了一个具有全局收敛性的原一对偶外点算法。结果：每步迭代利用Lagrange函数的鞍梯度构造搜索方向，生成次可行解序列，由此得到的序列的极限就是原-对偶问题的最优解。结论：即使从原一对偶问题的不可行点开始迭代算法也收敛。     

区间数线性规划问题的解法

基于区间数与实数之间的关系,提出了区间数线性规划的激进最优解,保守最优解的定义.利用约束集之间以及目标函数值之间的关系,在原有区间数线性规划的基础之上,给出了两个求解激进最优解、保守最优解的方法.数值例子验证了该方法的有效性和可行性.