线性规划单纯形法的三种实现形式探析  

The Three Form Tableaus of Simplex Methods Solving to the Linear Programming

作　　者：杨静蕾[1] 张建勇[1] 杨君泺 YANG Jing-lei;ZHANG Jian-yong;YANG Jun-luo(Business School, Nankai University, Tianjin 300071,China;College of Economic and Social Development, Nankai University, Tianjin 300071, China)

机构地区：[1]南开大学商学院,天津300071 [2]南开大学经济与社会发展研究院,天津300071

出　　处：《大学数学》2020年第4期68-73,共6页College Mathematics

基　　金：国家自然科学基金资助项目(NSFC 61772290)。

摘　　要：按照一般寻优算法原则,在定义可行方向和步长的基础上,从线性规划问题系数矩阵的列向量子空间出发,说明了单纯形法的顶点寻优过程是一个在约束条件的仿射空间和系数矩阵的零子空间交错前进的过程,并在此基础上归纳和总结了数据字典式单纯形表、经典单纯形表和简化单纯形表的实现形式及其迭代计算的特点和优势,并建议未来在《运筹学》教学中广泛推广这三种类型的单纯形表.Using the general processes of searching technique for optimization,the principle of the simplex method is demonstrated by the feasible direction and the optimal step size,which are key factors for optimization algorithms.It is shown that the process of extreme optimization is an alternation forward movement from the affine space of the constraints to the zero subspace of the constraint coefficient matrix in a linear programming.From this conclusion,three simplex tableaus are summarized and analyzed according to their characteristics and advantages.They are the dictionary simplex tableau,the classical simplex tableau and the simplified simplex tableau.We conclude that these three types of simplex tableaus could be integrated in the simplex method teaching practices to improve students’learning efficiency about the linear programming.

关 键 词：单纯形表 线性规划 向量空间 

分 类 号：O110.6150[理学—数学]