| dc.description.abstract | We investigate the use of interior point methods for solving quadratic
programming problems with a small number of linear constraints where
the quadratic term consists of a low-rank update to a positive semi-de nite
matrix. Several formulations of the support vector machine t into this
category. An interesting feature of these particular problems is the vol-
ume of data, which can lead to quadratic programs with between 10 and
100 million variables and a dense Q matrix. We use OOQP, an object-
oriented interior point code, to solve these problem because it allows us
to easily tailor the required linear algebra to the application. Our linear
algebra implementation uses a proximal point modi cation to the under-
lying algorithm, and exploits the Sherman-Morrison-Woodbury formula
and the Schur complement to facilitate e cient linear system solution.
Since we target massive problems, the data is stored out-of-core and we
overlap computation and I/O to reduce overhead. Results are reported
for several linear support vector machine formulations demonstrating the
reliability and scalability of the method. | en |
