Newton Method with AOR Iteration for Finding Large Scale Unconstrained Minimizer with Tridiagonal Hessian Matrices

Abstract

Finding the large scale unconstrained minimizer using Newton method has required the calculation of large and complicated linear systems results from solving the Newton direction. Therefore, in this paper, we propose a method for solving large scale unconstrained optimization problems with tridiagonal Hessian matrices to reduce the complexity of calculating Newton direction. Our proposed method was a combination of Newton method and Accelerated Over Relaxation (AOR) iterative method. To evaluate the performance of the proposed method, combination of Newton method with Gauss-Seidel iteration and Newton method with Successive Over Relaxation (SOR) iteration were used as reference method. Finally, the numerical experiment illustrated that the proposed method produce results that are more efficient compared to the reference methods with less execution time and minimum number of iterations.