Optimization and sampling problems over group orbits and their convex hulls, called orbitopes, capture various important problems in computer science, mathematics, and physics. For instance, the problem of finding minimum norm vectors in orbits has connections with scaling problems, linear programming, and testing algebraic identities; and the set of density matrices, central to semidefinite programming and quantum computing, is an orbitope. It turns out that several orbit problems, while not convex, are geodesically convex optimization problems. There are also deep connections between orbits/orbitopes and polytopes. Recent works have developed algorithms for a number of problems that leverage these connections and, crucially, the symmetry of the problems.
This workshop will focus on algorithms for computational problems related to orbits and orbitopes, and explore connections of these objects with theoretical computer science, discrete optimization, quantum physics, statistics, mathematics, and machine learning.
All events take place in the Calvin Lab auditorium.
Further details about this workshop will be posted in due course. Enquiries may be sent to the organizersworkshop-gm3 [at] lists.simons.berkeley.edu ( at this address.)