基于指数型核函数的线性规划原始对偶内点算法  

Primal-dual interior-point algorithm based on exponential kernel function for linear programming problems

作　　者：姚思及[1] 白延琴[1] 陶少哲[1] 郑仁[1] 周元诚[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2012年第2期193-202,共10页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11071158);上海市重点学科建设资助项目(S30104)

摘　　要：给出线性规划原始对偶内点算法的一个单变量指数型核函数.首先研究了这个指数型核函数的性质以及其对应的障碍函数.其次,基于这个指数型核函数,设计了求解线性规划问题的原始对偶内点算法,得到了目前小步算法最好的理论迭代界.最后,通过数值算例比较了基于指数型核函数的原始对偶内点算法和基于对数型核函数的原始对偶内点算法的计算效果.An univariate exponential kernel function of primal-dual interior-point algorithms for solving linear programming problems is proposed in this paper. First, the properties of the exponential kernel function and the corresponding bar- rier function are investigated. Then, the exponential function is applied to primal- dual interior-point algorithms for solving linear programming problems. The ite- ration bound for small-update methods is derived, and the best known bound is obtained, which is the same as that for the algorithm based on the logarithmic barrier function. Finally, several numerical examples are shown to compare the computational efforts of the algorithm based on the exponential function and the logarithmic function, respectively.

关 键 词：线性规划问题 原始对偶内点算法 障碍函数 

分 类 号：O221.1[理学—运筹学与控制论]