Solving linear programming problems by the interior-point method

Abstract

This research aims to survey methods of solving linear programming problems by the interior-point method in 3 approaches: Karmarkar's projective scaling, the primal affine scaling and the primal-dual algorithm. We construct a program by C++ language on the Windows operating system. In our results, we tested our program with our small problems and problems in MPS (Mathematical Programming System) files. Typically, if problem has a small size then our program uses iteration numbers of processing more than program which bases of the simplex method. If problem has a large-scale size then our program uses iteration numbers of processing less than program which bases on the simplex method.