Speaker #2 Abstract: In the first talk, you see some interesting applications of convex optimization. However, modeling a problem as a convex optimization problem would be useless without efficient algorithms for solving it. In the second talk, we see how to start solving a convex optimization problem.
In this talk, using a notion of majorization against unbounded traces, we characterize the norm-closed convex hulls of the unitary orbits of self-adjoint operators in any unital C*-algebra. Furthermore, for several classes of C*-algebras, such as those satisfying Blackadar's strict comparison of positive elements, an upper bound for the number of unitary conjugates in a convex combination required to approximate an element in the closed convex hull within a given error is shown to exist. (Joint work with P. Ng and L. Robert.)