Optimal hybrid BFGS-CG method for unconstrained optimization

Abstract

In solving unconstrained optimization problems, both quasi-Newton and conjugate gradient methods are known to be e cient methods. Hence, the optimal hybrid Broyden-Fletcher-Goldfarb-Shanno-Conjugate Gradient (OBFGS-CG) method is proposed in this work, which combines the strengths of both BFGS and CG methods. The optimal hybrid BFGS-CG method is based on an existing hybrid BFGS-CG method. The optimal BFGS-CG paramter, when utilised in solving unconstrained optimization problems, resulted in improvement in the total number of iterations and CPU time.