I adapted part of my PhD thesis intro into an educational writeup covering basic concepts and popular algorithms in nonlinear programming in a hopefully accessible way, targeted at people with some mathematical but not much optimisation background. I would appreciate your comments if you have some time to read it https://www.researchgate.net/publication/355362612_Some_popular_nonlinear_programming_algorithms.
I would like to thank @mbesancon for his comments on an early draft of this document which helped me significantly improve it. Of course, any mistakes in there are mine and mine only so please read with care.