What are applications of convex sets and the notion of convexity in mathematics and science?
This question have been already post as:
but I wanted to know the relationship with other sciences while previous mentioned questions can be correctly answered just as: for optimization theory.
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.