Optimization problems with sparse matrix cone constraints arise
naturally in a wide range of applications, and such problems can often
be solved efficiently by carefully utilizing the underlying structure.
Two kinds of sparse matrix cones are of particular interest: the cone of
symmetric positive semidefinte matrices with a given sparsity pattern
and its dual cone, the cone of sparse, positive semidefinite-completable
matrices. These cones are very general and include, as special cases,
the nonnegative orthant, the quadratic cone, and the cone of positive
semidefinite matrices. Using techniques from sparse numerical linear
algebra, the structure of the sparse matrix cones can be exploited to
construct faster optimization algorithms.. This talk will focus on the
usefulness of sparse matrix cone formulations, which will be
demonstrated through numerical examples drawn from a variety of problems
such as optimal power flow and robust estimation.