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Can you provide good references to the trust region dogleg method? This optimization method is used in Matlab's fsolve to solve nonlinear simultaneous equations and I want to understand it better.

I have noticed the list of references at the bottom of the Matlab help page but I'm lookng for something that gives a gentler introduction: more intuitive, not too mathematical and preferably with diagrams. I have a background in quantum physics, but am not so strong on numerical math.

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    Multi-variate nonlinear optimization by its nature is going to tend to be mathematical. Did you follow the link in the [Algorithms section](https://www.mathworks.com/help/optim/ug/fsolve.html#moreabout) of the documentation to read more about the [Trust-Region Dogleg Method](https://www.mathworks.com/help/optim/ug/equation-solving-algorithms.html#f51887)? Also, [this link](https://optimization.mccormick.northwestern.edu/index.php/Trust-region_methods#Dogleg_Method) was helpful for me and there are numerous other class notes and presentation available via Google – 2017-01-05

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Section 6.4.2 of the book "Numerical Methods for Unconstrained Optimzation and Nonlinear Equations" by J. E. Dennis and R. B. Schnabel gives a very readable description of the trust region approach using a single and double dogleg step. There are some figures, a worked out example, and pseudocode is provided in an appendix.