TITLE: Is group theory useful in any way to optimization?
QUESTION [7 upvotes]: For what I have seen, optimization uses a lot of linear algebra and convex analysis, but I have not seen any group theory being used, so I was curious about it. 
Is group theory useful in any way to optimization?

REPLY [5 votes]: Yes, certainly. Please search for the papers with keywords "symmetry breaking constraint programming" to find out more information. In particular, see Symmetry in Constraint Programming by Ian P. Gent, Karen E. Petrie, Jean-François Puget, Chapter 10 in Handbook of Constraint Programming, Edited by F. Rossi, P. van Beek and T. Walsh, Elsevier, 2006.
Basically, knowing symmetries of solutions allows to reduce the search space: if it is known that the property of being a solution to the problem is preserved under some symmetries, then we have to check only representatives of orbits of solutions with respect to these symmetries, and groups naturally occur in studying this.