A new modification of the quasi-newton method for unconstrained optimization

Hamsa Th. Saeed Chilmeran, Huda I. Ahmed, Eman T. Hamed, Abbas Y. Al-Bayati


In this work we propose and analyze a hybrid Conjugate Gradient (CG) method in which the parameter is computed as a linear combination between  Hager- Zhang [HZ] and Dai-Liao [DL] parameters. We use this proposed method to  modify  BFGS method and to prove the positive definiteness and QN-conditions of the matrix.Theoretical trils confirm that the new search directions aredescent directions under some conditions, as well as, the new search directions areglobally convergent using strong Wolfe conditions. The numerical experiments show that the proposed method is promising and  outperforms alternative similar CG-methods using Dolan-Mor'e performance profile.


BFGS method; Conjugate graient method; Dolan-mor'e performance; Globally convergence; Strong wolfe condition; Unconstrainedoptimization convex function

DOI: http://doi.org/10.11591/ijeecs.v21.i3.pp%25p
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