A new hybrid scaled search direction for unconstrained optimization

Abstract

The best spectral CG-algorithm which is introduced by (Birgin &Martinez) and (Andrei. N) is modified in this paper by a hybrid search direction to overcome the lackness positive definiteness of the matrix defining the search direction.Two successive scalar parameters are introduced in this paper which are satisfy QN-like condition.These parameters are combined in such away to give a hybrid scaled search direction.The new proposed algorithm is still global convergent both theoretically and numerically.Computational results for (43) unconstrained test functions(Andri.N)show that the new algorithm substantially outperform the well- known(Andrei.N) scaled algorithm including the spectral (Birgin & Martinez) algorithm