Linear programming with a feasible direction interior point technique for smooth optimization

We propose an adaptation of the Feasible Direction Interior Points Algorithm (FDIPA) J. Herskovits, for solving large-scale linear programs. At each step, solution two systems with same coefficient matrix is determined. This step involves a significant computational effort. Reducing time is, therefore, way to improve performance method. The be solved are associated definite positive symmetric matrices. Therefore, we use Split Preconditioned Conjugate Gradient (SPCG) method solve them, together Incomplete Cholesky preconditioner using Matlab’s ICHOL function. also first iteration conjugate gradient, and presolve before applying algorithm, in order reduce cost. Following, then provide mathematica proof that show iterations approach Karush–Kuhn–Tucker points problem under reasonable assumptions. Finally, numerical evidence not only works theory but competitive more advanced methods.