Curvature-based multistep quasi-Newton method for unconstrained optimization

Multi-step methods derived in [1–3] have proven to be serious contenders in practice by outperforming traditional quasi-Newton methods based on the linear Secant Equation. Minimum curvature methods that aim at tuning the interpolation process in the construction of the new Hessian approximation of the multi-step type are among the most successful so far [3]. In this work, we develop new methods of this type that derive from a general framework based on a parameterized nonlinear model. One of the main concerns of this paper is to conduct practical investigation and experimentation of the newly developed methods and we use the methods in [1–7] as a benchmark for the comparison. The results of the numerical experiments made indicate that these methods substantially improve the performance of quasi-Newton methods.