Trust-region image minimization

The only difference between the steps along the image mode and the transverse modes is the sign of the level shift. The level shift p < —A.i is determined such that the step is to the boundary of the trust region. Equation (6.18) forms the basis for the trust region image minimization (TRIM) method for calculating saddle points.20... 

To minimize the image function we use a second-order method since in each iteration the Hessian is needed anyway to identify the mode to be inverted (the image mode). Line search methods cannot be used since it is impossible to calculate the image function itself when carrying out the line search. However, the trust region RSO minimization requires only gradient and Hessian information and may therefore be used. In the diagonal representation the step Eq. (5.8) becomes... 

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