Bregman proximal methods for semidefinite optimization.

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.

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