Monday, January 02, 2012

Convexity as the one concept to bind them

A little bit more math to help us into the new year.
This article is really very nice:

What Shape is your Conjugate? A Survey of Computational Convex Analysis and its Applications (by Yves Lucet)

This article is beautiful because it brings together many, and I mean really many, algorithms and unifies them all through applied convex analysis. For example, there is something in common among:
  • Computing flows through networks
  • Properties of alloys
  • Image processing for  IRM, ultrasound, ...
  • Dynamic programming
The magic in back of all of these concepts is convexity and how certain  mappings preserve certain properties. The article is proabably a bit fast for many readers, but truly insightful because of the scope of its coverage. It really priovides a common way to approach convexity in its many different forms.