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
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?
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
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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?