Some advice on how to use the code.

subject to | (12.2) |

where is the local model of the objective function around , and . The size of the steps are limited by the trust region radius which represents the domain of validity of the local model . It is assumed that the validity of the local model at the point is only related to the distance and not to the direction of . This assumption can be false: In some directions, the model can be completely false for small and in other directions the model can still be valid for large .

Currently the trust region is a simple ball (because we are using the L2-norm ). If we were using the H-norm, the trust region would be an ellipsoid (see next Section 12.4 about H-norm). The H-norm allows us to link the

Since we are using a L2-norm, it's very important to scale correctly the variables. An example of bad-scaling is given in Table 12.1.

When all the variables are of the same order of magnitude, the optimizer is the fastest. For example, don't mix together variables which are degrees expressed in radians (values around 1) and variables which are height of a house expressed in millimeters (values around 10000). You have to

The same advice (scaling) can be given for the constraints: The evaluation of a constraint should give results of the same order of magnitude as the evaluation of the objective function.