Optimization | Convexity & Smoothness

Optimization | Convexity & Smoothness


My genuine gratitude goes to our amusing yet enlightening professor, Yuanzhi Li, for this fabulous course and all the lively delivered lectures.



I spent a considerable amount of time figuring out the following lemmas & problems.


I’ve already typed them out as decently organized formulae so I’ll dump them here for reference and some comments (if I’d come back with any).


Table of Contents



(1) defined over a convex set

(2) 2nd order differentiable

(3) hessian condition: second order derivative is semi-positive definite

(4) lower linear bound



(1) doesn’t require convexity

(2) constrained on speed of “growth”

(3) hessian condition: second derivative has a numeric positive finite upper bound

(4) upper quadratic bound