Karmarkar's method for nonlinear programming problems

number: 
431
إنجليزية
Degree: 
Imprint: 
Mathematics and Computer Applications
Author: 
Wifaq Ghazi Abdul-Raheem Al-Ani
Supervisor: 
Dr. Alaudin N. Ahmed
Dr. Fadhil A. Al-Baidhani
year: 
2000
Abstract:

Linear programming problems with large number of variables were found to be efficiently solved by Karmarkar's algorithm. In this thesis Karmarkar's algorithm is analyzed in detail and applied to linear programming problems. Also Karmarkar's method is extended to solve nonlinear problems with convex function and linear constraints. The proposed extension is tested and the results are analyzed. The method presented consists of finding best direction to the optimal solution through minimizing the function of the tangent plane at each iteration step. In Karmarkar's method parameters namely ά , μ and Acc. are studied through hundreds of runs for different examples. Also a direct iterative method for solving objective functions with unknown minimum is introduced with full algorithm details. It is found that the methods presented successfully solved the problem Higher accuracy required the choice of proper values for the parameters ά, μ, Acc. For good results in NLP problems lower values for ά are suggested (0.05-0.15).