A Fourth-Order Nonlinear Conjugate Gradient Method in Large Scale Optimization

This paper is presenting a fourth-order nonlinear conjugate gradient method in large scale optimization. This method solves unconstrained optimization problems. It is based on a nonlinear polynomial approximation of the objective function. The idea is to approximate the minimizing function by Taylor series development using fourth-order terms. The algorithm is presented in steps and some properties of the gradients are proved, using classical results. Also, the convergence analysis has been proved under known assumptions. Some numerical results have been compared to existing data. The analysis of these results confirms that the new method is accurate, since the computed results are very close to the exact solutions.