3.2 Smooth and Strongly Convex Functions

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  1. Constantine Caramanis
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For anyone interested in understanding smooth/strong convexity conceptually:
A function is smoothly convex if at any point you can fit a quadratic on it
A function is strongly convex if at any point you can fit a quadratic underneath it

gt_money
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Thank you for sharing such a good video!

andrewmeowmeow
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thank you so much this is really useful thanks for saving my finals and everything

lindseyfeng
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Assumptions: 5:30
Beta-Smooth(Lipschitz continuous): 8:00
Beta-smooth -> monotone -> convex: 10:31
Beta-smooth -> quadratic upper bound 15:48
Alpha-Strong convexity -> quadratic lower bound: 22:43

xinlunzhao
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Thanks so much for these detailed explanations. It really helps.

salwamostafa
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Does the definition of the quadratic upper bound assume that f is convex? from what I understand that f is not required to be convex just smooth, but to derive the quadratic upper bound we define the function g and proved that g is convex.

Another question, why did we define function g in that exact shape?

eyadshami