A stable symmetrization of the linear systems arising in interior-point
methods for solving linear and semidefinite programs is introduced. The symmetrization
includes a novel pivoting strategy to minimize the norm of the right and side.
the search directions generated by the iterative solver will have
fairly low relative accuracy, a new interior-point approach
based on low accuracy search directions is presented
and analyzed. In the numerical examples, this approach results in
a surprisingly small number of outer iterations, indicating that
the interior-point concept may also be suitable
for ill-conditioned problems for which it is difficult to compute
high accuracy search directions.
An application with doubly nonnegative matrices concludes the talk.