- Juan Peypouquet
- Rijksuniversiteit Groningen
- Systems and Control
First order optimization methods and their acceleration.
In 1744, Leonhard Euler said: Nothing in the world takes place without optimization, and there is no doubt that all aspects of the world that have a rational basis can be explained by optimization methods. In Euler's view, optimization is the art of making rational decisions. In order to find minimizers of a convex function, many contemporary algorithms produce sequences of approximate solutions in such a way that the value of the function decreases at each iteration. This seems quite natural, since convex functions have no critical points other than their global minimizers. In this talk, we will see how the performance of first order optimization methods can actually be improved by allowing them to break the rational paradigm of successive decrease.