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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.

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I've converted this from a comment to an answer since no one produced any more elaborate answer.

Yes, there is a certain arbitrariness. The values you commonly see in books and papers are ones which seem to work well over some reasonable range of problems. They are not handed down from god, and you may be able to be to do better for some problems.

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  • $\begingroup$ But there is another issue I am facing in using this algorithm, not only the parameters have an arbitrariness associated with them, the rules for updating the trust region radius in itself are defined vaguely. And hence all these choices for parameters and the update rules don't sound convincing. Are there any ways to find out what are the regions of the validity of these values? $\endgroup$
    – exp iㅠ
    Oct 8, 2015 at 5:35
  • $\begingroup$ Valid regions of validity come down to convergence proofs. There's considerable latitude in update rules and parameter values while still maintaining convergence proofs. Therefore it comes down to rules and values which seem to work well over the range of problems which the author dealt with, and building on folklore and experience over the years. Most folks start off with rule and values recommended by prominent authors and developers, and perhaps consider tweaking from there, if at all. For example, rules and values in the well known book springer.com/us/book/9780387303031 . $\endgroup$
    – Mark L. Stone
    Oct 8, 2015 at 14:29

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