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.
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.
There's a fascinating link between minimization of quadratic functions and polynomials. A link
deep and allows to phrase optimization problems in the language of polynomials and vice versa.
Using this connection, we can tap into centuries of research in the theory of polynomials and
shed new light on …