I was watching the trust region algorithm implementation in the dlib code, optimization_trust_region.h, where it is stated that it is stated that "This is an implementation of algorithm 4.3 (Trust Region Subproblem) from the book Numerical Optimization by Nocedal and Wright. Some of the details are also from Practical Methods of Optimization by Fletcher." I started to compare both algorithms and found mismatch which I can't explain. The heart of the algorithm is the 1-d root-finding procedure for some scalar function \phi. The formulae for the iteration step mismatch and that's how (sorry, first I thought I can post my question with LaTeX-style formulae here, but it turned out this is impossible, so I am forced to post a screenshot instead):
How could one make sense of the discrepancy? Could both approaches be correct, and how?
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Your question is off-topic here, as it is not directly code-related. Better places would be [scientific computing SE](https://scicomp.stackexchange.com), [learning math SE](https://math.stackexchange.com) or perhaps even [research math](https://mathoverflow.net) – Lutz Lehmann Feb 17 '20 at 21:15
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I disagree, as the question is directly connected with the dlib code. Moreover, the question itself is posed not about mathematics per se, but about implementation in the code. – Dan Feb 18 '20 at 06:55
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It is a question on the design and implementation of an algorithm. That is the (or one of the) core topic of scicomp.SE. There you will also find mathjax enabled, which should implicitly tell you about the intentions of the creators. – Lutz Lehmann Feb 18 '20 at 09:05