The Importance of Step Control in Optimization Methods

The restricted step algorithm is described and applied to structure minimization. Robust solutions for the associated root-finding problem are derived. Structure minimizations employing the rational function optimization and the restricted step algorithm in the framework of the quasi-Newton method are compared. With approximated start Hessians both methods show a very similar performance. However, if the start Hessian matrix is calculated the restricted step algorithm is more reliable than the rational function optimization for the studied structure minimizations.