Conjugate gradient and steepest descent approach on quasi-Newton search direction

Abstract

Abstract. An approach of using conjugate gradient and classic steepest descent search direction onto quasi-Newton search direction had been proposed in this paper and we called it as 'scaled CGSD-QN' search direction. A new coefficient formula had been successfully constructed for being used in the 'scaled CGSD-QN' search direction and proven here that the coefficient formula is globally converge to the minimizer. The Hessian update formula that has been used in the quasi-Newton algorithm is DFP update formula. This new search direction approach was testes with some some standard unconstrained optimization test problems and proven that this new search direction approach had positively affect quasi-Newton method by using DFP update formula.