基于Lemke算法的大学数学线性互补方程  

Teaching of Linear Complementary Equation in College Mathematics Based on Lemke Algorithm

作　　者：陈婷婷[1] 张亚[2] CHEN Tingting;ZHANG Ya(Youth League Committee,Chuzhou City Vocational College,Chuzhou 239000,China;Public Teaching Department,Chuzhou City Vocational College,Chuzhou 239000,China)

机构地区：[1]滁州城市职业学院团委,安徽滁州239000 [2]滁州城市职业学院公共教学部,安徽滁州239000

出　　处：《玉溪师范学院学报》2022年第6期7-15,共9页Journal of Yuxi Normal University

基　　金：滁州城市职业学院2020年度人文社会科学重点项目(2020sk07);2019年滁州城市职业学院重点教研项目(2019jyxm06)。

摘　　要：基于Lemke算法,提出求解二次规划广义互补主元算法.通过行初等变换,不需选择出基变量和人工变量,简化了Lemke主元算法.通过分析Lemke互补转轴算法,求解含有等式约束凸二次规划问题出现退化原因,对Lemke算法迭代步骤进行修正,分析了该算法求解含有等式约束的凸二次规划问题的有效性.Based on Lemke algorithm,this paper discusses and analyzes the teaching of linear complementary equations in college mathematics,and puts forward a generalized complementary principal element algorithm for solving quadratic programming.Through elementary transformation,the optimal solution can be obtained in the same table without selecting the base variables and artificial variables,which simplifies Lemke principal element algorithm.By analyzing Lemke complementary rotating axis algorithm,the reasons for the degradation of convex quadratic programming problems with equality constraints were solved,the iterative steps of Lemke algorithm were modified,and the effectiveness of Lemke algorithm to solve convex quadratic programming problems with equality constraints was analyzed by using the improved Lemke algorithm.In view of the characteristics and teaching practice of linear complementary equation course based on Lemke algorithm,the algorithm of practical problems is solved through the implementation of algorithm design teaching in the teaching process.

关 键 词：Lemke算法 教学 线性互补方程 二次规划 

分 类 号：O221.2[理学—运筹学与控制论]