New Self-scaling Quasi-Newton methods for unconstrained optimization

The quasi-Newton technique is one of the most well-known iterative solutions for unconstrained optimization problems. The quasi-Newton techniques are known for their high accuracy and rapid convergence. In this paper, we derive four self-scaling BFGS methods. The Wolfe line search criteria define the step size selection. The method of global convergence is demonstrated when the objective function is uniformly convex. Preliminary computational tests on a set of 30 unconstrained optimization test functions suggest that this technique is more efficient and resilient than implementing the non-scaled version of the BFGS. In terms of iteration count and function/gradient evaluations, comparative findings reveal that the suggested strategy is computationally efficient.