基于LU分解的亏基摄动对偶Ⅰ阶段算法  

A Phase-Ⅰ Algorithm Based on the Perturbation and Deficient-basis with LU Factorization

作　　者：马艳琴[1] 张利利 卜春霞[2] 

机构地区：[1]黄河科技学院数理部,河南郑州450063 [2]郑州大学数学系,河南郑州450001

出　　处：《数学的实践与认识》2017年第17期289-294,共6页Mathematics in Practice and Theory

基　　金：河南省教育厅基础研究资助项目(17B110001)

摘　　要：将摄动算法和亏基单纯形算法相结合,以充分发挥这两种算法的优势,从而为亏基对偶单纯形算法提供一个新的Ⅰ阶段算法,以使其进一步克服退化所带来的困扰.数值试验结果表明,新算法能够降低退化带来的不良影响,减少总迭代次数和运算时间,其效率不仅远远优于传统的单纯形算法,且优于原有的亏基单纯形算法,是一个非常吸引人且充满希望的新尝试.The purpose of this thesis is to combine the perturbation algorithm and deficientbasis algorithm to bring the advantages of the two types of algorithms into full play, consequently offer a new Phase-1 procedure for the dual deficient-basis algorithm, and overcome the difficulties from degeneracy to a higher extent. Our computational experiments show that the proposed algorithms reduce total number of iterations significantly. New algorithms＇ s efficiency is superior not only to the conventional simplex algorithm but the deficient-basis algorithm. So this is a very attractive new approach being full of promise.

关 键 词：单纯形法 亏基 退化 摄动 LU分解 

分 类 号：O224[理学—运筹学与控制论]