How good is a Broyden-Fletcher-Goldfarb-Shanno-like update Hessian formula to locate transition structures? Specific reformulation of Broyden-Fletcher-Goldfarb-Shanno for optimizing saddle points

摘要

Based on a study of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) update Hessian formula to locate minima on a hypersurface potential energy, we present an updated Hessian formula to locate and optimize saddle points of any order that in some sense preserves the initial structure of the BFGS update formula. The performance and efficiency of this new formula is compared with the previous updated Hessian formulae such as the Powell and MSP ones. We conclude that the proposed update is quite competitive but no more efficient than the normal updates normally used in any optimization of saddle points. (C) 1998 John Wiley & Sons, Inc. [References: 32]