Numerical experience with a class of self-scaling quasi-Newton algorithms

Self-scaling quasi-Newton methods for unconstrained optimization depend upon updating the Hessian approximation by a formula which depends on two parameters (say, τ and θ) such that τ = 1, θ = 0, and θ = 1 yield the unscaled Broyden family, the BFGS update, and the DFP update, respectively. In previous work, conditions were obtained on these parameters that imply global and superlinear convergence for self-scaling methods on convex objective functions. This paper discusses the practical performance of several new algorithms designed to satisfy these conditions.