What are applications of convexity in sciences?

Question

What are applications of convex sets and the notion of convexity in mathematics and science?

This question have been already post as:

• What are the applications of convex sets?
• What are the main uses of Convex Functions?

but I wanted to know the relationship with other sciences while previous mentioned questions can be correctly answered just as: for optimization theory.

Answer 1

Convexity is important in quantum information theory. Take a look at

• Ingemar Bengtsson, Karol Zyczkowski, Geometry of quantum states: an introduction to quantum entanglement, Cambridge University Press, December 2007.

• John Watrous, Semidefinite programming in the theory of quantum information.