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In solving large scale problems, the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Hence, a new hybrid method, known as the BFGS-CG method, has been created based on these properties, combining the search direction between conjugate gradient methods and quasi-Newton methods. In comparison to standard BFGS methods and conjugate gradient methods, the BFGS-CG method shows significant improvement in the total number of iterations and CPU time required to solve large scale unconstrained optimization problems. We also prove that the hybrid method is globally convergent

The Hybrid BFGS-CG Method in Solving Unconstrained Optimization Problems