I have a question concerning the update algorithms used for the Hessian during optimizations and transition state searches. In a paper by J.Baker (J.Comp.Chem 7, 385-395 (1986)) and some manuals (Games, Gaussian) the statement is made that while the BFGS update is *better* for an optimization, for a transition state, search the DFP update is to be preferred. Of course, no reason is provided to support this statement. One of the books frequently referred to (Fletcher: Practical Methods of Optimization) makes the following statements: - Provided that the function being optimized is quadratic AND the line-search is exact, positive definiteness of the Hessian is preserved (for both DFP and BFGS formulas) - For inexact line searches, global convergence of the BFGS method has been proved. However, for the DFP this could not be shown. Is this somehow related to the fact that for TS searches, the DFP-method is recommended? Why is this so? Does this mean that the BFGS method will lead to a positive-definite Hessian, even if the initial Hessian has the required negative eigenvalue? Any hint is appreciated! Thanks,
Dear Manish Kumar Sahu,
I suggest you to see links on topic.
https://ir.canterbury.ac.nz/bitstream/handle/10092/12137/byatt_coope_price_ucdms2003-1_report.pdf;sequence=1
https://www.cs.purdue.edu/homes/jhonorio/16spring-cs52000-quasinewton.pdf
http://www.spindynamics.org/documents/cqc_lecture_6.pdf
Best regards
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