(2.18) |

The simple algorithm described in the Section 2.2 can be generalized as follows:

**Initialization**An initial point and an initial trust region radius are given. The constants , , and are also given and satisfy:and (2.19)

Compute and set**Model definition**Choose the norm and define a model in**Step computation**Compute a step that ''sufficiently reduces the model'' and such that**Acceptance of the trial point.**Compute and define:(2.20)

If , then define ; otherwise define .- Trust region radius update. Set
(2.21)

Increment by 1 and go to step 2.