Recently, Al-Baali (2014, 2004) has extended the damped-technique in the modified BFGS method of Powell for constrained optimization to the Broyden family of quasi-Newton methods for unconstrained optimization. Appropriate choices for the damped-parameter which maintains the convergence property of these methods will be proposed. Numerical results will be described to show that these choices improve the performance of quasi-Newton methods substantially in several cases.

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