Application of Newton-4EGSOR Iteration for Solving Large Scale Unconstrained Optimization Problems with a Tridiagonal Hessian Matrix

Abstract

Solving the unconstrained optimization problems using Newton method will lead to the need to solve linear system. Further, the Explicit Group iteration is one of the numerical methods that has an advantage of the efficient block iterative method for solving any linear system. Thus, in this paper to reduce the cost of solving large linear system, we proposed a combination between Newton method with four-point Explicit Group (4-point EG) block iterative method for solving large scale unconstrained optimization problems where the Hessian of the Newton direction is tridiagonal matrices. For the purpose of comparison, we used combination of Newton method with basic iterative method namely successive-over relaxation (SOR) point iteration and Newton method with two-point Explicit Group (2-point EG) block iterative method as reference method. The proposed method shows that the numerical results were more superior compared to the reference methods in term of execution time and number of iteration.