1. Lipschitz Continuity: The “Speed Limit”
This assumption prevents the function from changing too rapidly over a certain distance.
2. 𝐿-Smoothness: The Curvature Ceiling
Smoothness ensures the gradient (slope) of the function doesn’t change abruptly. A function is 𝐿-smooth if its gradient is Lipschitz continuous.
3. 𝜇-Strong Convexity : The Curvature Floor – Bowl Shape
Strong convexity guarantees that the function has a minimum “bowl” shape and is not flat.
https://arxiv.org/pdf/2110.15470#:~:text=1%20Introduction,(1.2)
https://www.stat.purdue.edu/~wang4094/resources/slides/2021_spring_DL_meeting_01_opt_basics.pdf
https://mitliagkas.github.io/ift6085-2020/ift-6085-lecture-3-notes.pdf