A FOURTH-ORDER NONLINEAR CONJUGATE GRADIENT METHOD AND TRUST REGIONS IN UNCONSTRAINED OPTIMIZATION

E. NWAEZE, L. O. OMENYI

Abstract


This paper presents a fourth-order nonlinear conjugate gradient method and trust regions in unconstrained optimization. The method has been designed to solve unconstrained optimization problems with high accuracy. It is based on a nonlinear polynomial approximation of the objective function. The idea is to approximate the minimizing function byTaylor series expansion using fourth-order terms. The algorithms are presented by steps and some properties of the gradients are proved, using classical results. Also, the convergence analysis has been proved under classical and known assumptions. The main algorithm generates adequate trust region radius iteratively and has a global convergence property. Numerical results are presented and compared to some existing results by Dolan Moore’s performance profile. The analysis of results confirms that this method is accurate, since the computed results are very close to the exact solutions.

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