In a trust region based Newton method, a number of constants are given as inputs to the algorithm that determine the updating rules for the trust region bound. Are these constants chosen arbitrarily or are there some rules that govern these constants.
For instance refer to this paper http://www.csie.ntu.edu.tw/~cjlin/papers/logistic.pdf On page 5 (631 in the article) there are a set of equations marked as 10, that determine the trust region bound. In these set of three equations there are 5 constants being used. Though the values of these constants used by the writers are specified on page 9 (635 in the article) however the choice seems to be rather arbitrary and I couldn't find any general rules to set these parameters.