Scientific Computation and Applied & Industrial Mathematics: Jack Poulson

While large numbers of researchers have investigated efficient distributed-memory schemes for dense and sparse-direct linear algebra, relatively little work has been performed on extensions into the important fields of conic optimization and lattice reduction. (Perhaps surprising) performance barriers for distributed sparse Second-order Cone Programs will be discussed, and a case will be made for defaulting to explicitly storing quasi-constant edge-degree plus low-rank decompositions of the sparse KKT systems and then solving said systems via applying the iteratively-refined inverse of an a priori regularized, Symmetric Quasi-Semidefinite factorization as a preconditioner for Flexible GMRES(k). Recent work towards high-performance variants of lattice reduction schemes (LLL and BKZ 2.0) will also be briefly discussed to help make the case for the importance of high-precision arithmetic. Some practical issues related to the implementation of these techniques within the open source library Elemental (https://github.com/elemental/Elemental) will also be discussed.