PSB-update

There Eire other Hessian updates but for minimizations the BFGS update is the most successful. Hessism update techniques are usually combined with line search vide infra) and the resulting minimization algorithms are called quasi-Newton methods. In saddle point optimizations we must allow the approximate Hessian to become indefinite and the PSB update is therefore more appropriate. 

It is for this reason the positive definite BFGS update Eq. (3.35) is preferred over the PSB update Eq. (3.33) for minimizations. The positive definite Newton step is usually a better direction than steepest descent since it takes into account features of the function further away from xc than does steepest descent. 

The Murtaugh-Sargent update, which was already discussed in Section 10.3.1, is one option [79,130,131]. Another common choice is the Powell-symmetric-Broyden (PSB) update, which was hrst recommended for TS optimization by Simons et al. [132]. A PSB updated Hessian is given by... 

The above update formula is known by the name PSB update (Povell s... 

Bofill [79,89,129-131,133] has developed a hybrid updating scheme with better performance for TS optimization. The Bohll update mixes MS and PSB solutions giving... 

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