“准最优基”程序实现与应用探讨  

Program Realization of "Quasi-Optimal Basis" and Its Application Discussion

作　　者：杨欢[1] 陶凤玲[1] 李若东[1] 高霞[1] 李积花[1] 

机构地区：[1]青海大学水利电力学院,青海西宁810016

出　　处：《数学的实践与认识》2014年第20期219-227,共9页Mathematics in Practice and Theory

基　　金：江苏省水利动力工程重点实验室资助项目(K13022)

摘　　要：在利用"准最优基"简化单纯形法的求解过程的基础上,采用matlab将"准最优基"方法程序化,并采用程序进行了模型.求解原采用两阶段法求解的线性规划问题,用"准最优基"方法,不必加入人工变量,改两阶段为一阶段,简化了求解过程,并针对只能将其目标函数系数为正的变量进基、约束条件都为正的局限性进行了探讨."准最优基"方法对目标函数的系数有正有负的情况,约束条件的系数有正有负的情况都适用.借助"bland法则"的思想,按下标顺序进基取代变量强度系数进基,得出了同样的结果,并对E.Beale的循环例子进行计算,一步得出最优解."准最优基"方法既可以提高运算速度,同时具有很好的适用性.Based on using ＂quasi-optimal basis＂ to reduce seeking solution progress of simplex method,using matlab to make ＂quasi-optimal basis＂ programmed and did model solution with it.Using program of ＂quasi-optimal basis＂ to solve linear programming problems replace of original two-phase method,there have no need of man-variable and predigested the progress of seeking solution,the limitations are discussed.It is also used to solve model that there are positive and negative in object function and constraint condition.Replacing order of strength coefficient with subscript by means of thought from ＂bland rule＂,got the same result,and solved the cyclic example of E.Beale with one step.Method of ＂quasi-optimal basis＂ improve the operation speed and has a good applicability.

关 键 词：线性规划 单纯形法 准最优基 两阶段法 

分 类 号：O221.1[理学—运筹学与控制论]