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On the Link Between Optimization and Polynomials, Part 3

A Hitchhiker's Guide to Momentum.

I've seen things you people wouldn't believe.
Valleys sculpted by trigonometric functions.
Rates on fire off the shoulder of divergence.
Beams glitter in the dark near the Polyak gate.
All those landscapes will be lost in time, like tears in rain.
Time to halt.

A momentum optimizer *

On the Link Between Optimization and Polynomials, Part 2

Momentum: when Chebyshev meets Chebyshev.

An analysis of momentum can be tightened using a combination Chebyshev polynomials of the first and second kind. Through this connection we'll derive one of the most iconic methods in optimization: Polyak momentum.