4.1.9 Comparison of Step Length and Trust Region Methods

Step length and trust region algorithms have in common that the next iteration point is selected according to a scalar value; in step length algorithms this scalar is the step length $\alpha_{k}$, in trust region methods this scalar is the size of the trust region. The major difference is how the second order information has influences on the search direction. Step length algorithms leave the Hessian unchanged while trust region methods use a so called ``modified'' Hessian.