Modified Interior Point Method Involving Choice Of Parameter For Linear Programming

The internal point method is one of the most effective algorithms to solve optimization problems.Since Karmarkar proposed the inner point method of the first polynomial time in 1984,after more than 30 years of continuous development,has achieved fruitful results.Now,inner point method has been successfully applied to many optimization problems,such as,linear programming,convex programming,complementary problem,semidefinite program-ming,etc.Researchers have developed many optimized software packages based on the internal point algorithm and have been widely used.When solving the linear programming problem with the internal point method,need to find the direction and step of the next iteration.First,determine the direction by solving Niudunfangcheng.How to solve this equation system easily and effectively is particularly important.Existing direct methods and iterative methods,direct methods such as Gaussian elimination method,Cholesky decomposition,etc.But these methods have large storage capacity,CPU time,and when solving large problems,they will encounter dense or pathological coefficients.This paper is divided into four chapters,the first chapter describes the background of the problems considered in this paper,the domestic and foreign research status and the frame struc-ture of the full text.The second chapter presents the problem and gives the algorithm to solve the problem.The third chapter analyzes the convergence and complexity of the algorithm.The fourth chapter analyzes the numerical experiment results and summarizes the full text.