Lieven Vandenberghe - University of California, Los Angeles (UCLA), Electrical Engineering We discuss first-order methods for semidefinite optimization, based on non-Euclidean projections and proximal operators, defined in terms of generalized (Bregman) distances. The goal is to avoid expensive eigenvalue decompositions, which limit the scalability of classical proximal methods when applied to semidefinite programs. We are particularly interested in techniques for exploiting sparsity and other types of structure that are common in control and signal processing, such as Toeplitz structure. This will allow us to apply extensions of the primal-dual hybrid gradient method to certain classes of large-scale semidefinite programs.