fsolve: difference between dogleg trust-region and Powell's dogleg methods?

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pluton schmidt 2023-3-10

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https://ww2.mathworks.cn/matlabcentral/answers/1926740-fsolve-difference-between-dogleg-trust-region-and-powell-s-dogleg-methods

编辑： pluton schmidt 2023-3-13

Matlab's help on the command `fsolve` for systems of nonlinear equations is not very clear. It seems to be by default a trust-region dogleg method [1], that is a trust-region method with a dogleg strategy relying on Powell's dogleg method [2]. However, from [2], Powell's dogleg method itself relies on an explicit trust region. It very much looks like a snake biting its tail. Are there clear explanations somewhere about the difference between dogleg trust-region methods and Powell's dogleg methods (also called Hybrid Powell)?

[1] Matlab trust-region dogleg

[2] Powell's dogleg method