文献类型：期刊文献

中文题名：基于逐步降阶的线性规划的单纯形算法

英文题名：A Simplex Method Base on Reducing the Constraint Conditions of Linear Programming

作者：高引民[1];陈建斌[1]

第一作者：高引民

机构：[1]北京联合大学商务学院

第一机构：北京联合大学商务学院

年份：2017

卷号：38

期号：4

起止页码：409-413

中文期刊名：中北大学学报：自然科学版

收录：北大核心:【北大核心2014】；

基金：国家自然科学基金资助项目(71572015)

语种：中文

中文关键词：线性规划;单纯形算法;约束条件;最优紧约束条件

外文关键词：linear programming; simplex method; constraint conditions; optimal tight constraint conditions

摘要：为完善线性规划约束条件方面的基本理论,研究了一种高效的求解线性规划问题的算法.以区分最优松约束条件和最优紧约束条件为主线,利用线性规划,线性代数等数学理论,进行分析,并通过大量的数据实验进行验证.从理论上获得了最优紧约束条件一些性质及识别最优松约束条件的定理,提供了一种新的单纯形算法.数据试验和理论上表明,在求解大规模解线性规划问题时,利用新的求解算法,使得模型逐步降阶,能达到求解的高效率.
Aiming to improve the theory of linear programming with respect to the constraint conditions, a new simple method in solving the large-scale problem ineffective variables was presented. Methods to study the property of optimal slack constraint conditions and optimal tight constraint conditions emplo- ying some mathematical tools in linear programming and linear algebra and so forth were used to do numerical tests. The characteristics of the optimal tight constraint conditions, the theorems of identifying optimal slack constraint conditions and a new simple method have been obtained from results. Numerical tests and theory illustrated that identifying and eliminating optimal slack constraint conditions can simplify its constraint conditions and improve the efficiency of solving the problem of linear programming in solving the large-scale problem.