Krasnosel’skii-Mann Iteration

an elegant and powerful abstraction

Abstraction is a key concept in computer science. Its utility extends also developing optimization tools. An elegant example is fixed point iteration.

As stated on Wikipedia:

Abstraction is the process of generalizing concrete details, such as attributes, away from the study of objects and systems to focus attention on details of greater importance.

When it comes to discussing convergence of optimization algorithms, we can often check if the update formula corresponds to an averaged operator and then appeal to key results in operator theory. Here is a set of slides I put together for a lecture on fixed point iteration, going beyond the classic result of Stefan Banach.

Enjoy.